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TABLE S 

DE S I N U S > 

TANGENTES» 

ET SECANT E^S, 

E T D E 

LOGARITHMES 

DES SINUS, TANGENTES, 

Et des Nombres depuis l'unité 
ju{c]^ues à looob. 

A'vec une Méthode pour refondre tres-faci- 
lement par leur moyen tous les Triantes 
Reéiilignes & Spheriques , & plufieurs 
^ueJHons AjirQnomiques. 

Par A^V L AC Q. 

Dernière Edition , corrigée & augmentée. 




A PARIS, 
Chez Jean Jombert, prés des Auguftins, 
i l'Image Nâcrc-Dame. 

M D- C I C. 
ÂFEC PRirilEGE DV ROT. 






/ 



■ N 



CHAPITRE PREMIER. 

DE WSAGE VB CES TABLES. 

CE traité contient une double 4iftinâion df 
tables t £n la première y celle des Sinus , Tan^ 
t Rentes , & Sécantes > de chaque degré Se minute du 
;;^ quart de Cercle , dont le demi • diamètre cft de 
^jnoooôôoo parties : enlèmble let Logarithmes d^ 
j^ Sinus Se Tangentes , obmettaht expreflement ceux 
^ des Sécantes , parce que fans lés Sécantes les calculs 
r de la Trigonométrie ie font de pateille fkdKté. £b 
ry l'autre 5 celle des Logarithmes pour les nombres ab- 
\ Iblus depuis lunité jufques i toooo. 
^ On peut pat le nàoyen de ces tables refbûdrre tout 
^ triangle en deuk manières » fçavoit parles notnbres 
Vulgaires des Sinus > Tangentes > Se Secaktts > ou pat 
leurs Logarithmes. 

En la Règle de trois , ta diSêrem^e du calcul trigoH 
hômetrique par nombres vulgaire&>& pat Logarithmes> 
tft tellci 

Voulant calculer par nombres vuleaitës » il faut mul- 
tiplier le fécond nombre parlé troiuéme , Se divifer le 
produit par le premier 2 le quotient fêta le quatrième. 
Mais , (i on veut calculer par leurs Logarithmes > 
il faut ajouter le Logarithme du fetondavec le Loga^ 
tithme du troifiéme , Se ôter de la fomme le Logaricb- 
me du pretnier: le nôtnbte reftaurferalelogarithose 
du quatrième , lequel étant cherché dans la première 
ou dans la dérniete Table ( félon qu'en fèta la nanite) 
donnera le quatrième requis. ^ 

Cette manière eft beaucoup plus facile que l'autre » 
princip^cment aux refolutiods de tous les Triangles 
Spheriques > car aux scfoluciori» de plttikuts Trian^tt. ^ 



'4 ChAV. h De Vufage de ces Tailes. 
leâilieties» coitimede la 3. 4. (?• Prop. &c. ileftp!as 
aisé d ufer de l'autre manière, ce que je laKTe à la àiù 
cretion des calculeurs. 

Or daucaut que la dernière Table contient feule- 
ment les Logarithmes des nombres depuis l'unité juf- 
qucs à looop , je montreray comment on pourra trou- 
ver le Logarithme d*un nombre qui fera entre loooo 
€c 10060000 , fie au contraire. 

1. Chercl\ez dans la dernière Table. le Logarith- 
itic des quatre premières figures du nombre donné. 

2. Otez le Logarithme trouvé du Logarithme im* 
mediatement fuivant eh la Table , pour avoir leur 
différence; 

f. Multipliez la différence trouvée , par les figures 
xeftantes du nombre donné) 5c coupez du produit vers 
h main droite autant de figures qu'il en fera rcfté^ 

4. Ajoutez le refte du produit au Logarithme. pre- 
.mierénicnt trouvé , la fomme fera le Logarithme re- 
quis , fi l'on change la première figure , qui doit tou^ 
jours être moitidre d'une unité que le nombre des fi«> 
gures , dont le nombre entier donné coniîflc. 
' Exemple. Qu'il faille' trouver le Logarichine de 
35^7^9^* Premièrement je trouve le Logarithme de 
35/Î7 , qui efl 3. 552.3031 : lequel étant ôté de 3. 55241489 
•la ckffcrence fe trobve iitj , laquelle étant multipliée 
par S94 ( les trois figures refiantes ^ } le produit dk 
1087998 » dont trois figures étans coupées y il refte 
,1087, qui étans ajoutez auLogarithme3. 55130,^1, la 
(bmme efl3 5524118 Enfin la première figure3. étant 
changée' eh ^ , le Logarithme du nom1)re donné 
'35^7'94 cfl <>i 5514118. . . ] 

Ainfi le Logarithme de ii^6oy t(ï y 0990157: &C 
de 1358009 le Logarithme cfl: 6. jji^^^^. 
Remarque. 

Etant donné, le nombre ir^^ : ou z^SL^l^i ou 

35$^^~ ,&c. leurs Loganthmes font les mêmes quecc- 

Ju^ du nombre entier ^5(77894 , horfmis la première 



CnAV. !• De Vnfage de ces TaHeu 5 

figure, (çavoir o. 5514118 : i. 55x4118. 2. 5524118, &c« 
& pour les troviver il n'y a aucune difFcrence. 

Et fi un nombre entier avec une fraftion décima- 
le, n'ayant en tout plus de 4 figures, eft donné, on 
trouvera (pn Logarithme cxaftemenc dans la mèmfc 
Table. Comme de 3-^£-, ou l^-^^.oxi 35677 > les Lo- 
garithmes fe trouvent vis à vis le nombre entier 3567-, 
en changeant feulement la première figure , comme 
il a été dit cy-deflus. 

Mais fi une autre efpcce de fradion eft jointe a un 
inombre entier, reduifez ce nombre-là àunefradtion 
impropre , & ôtcz le Logarithme du Dénominateur 
du Logarithme du Numérateur , le refte eft le Loga- 
rithme requis. 

Comme 3I étant réduit,il vient, -|-, donc o. <302c(^oo 
( le Logarithme de 4) étant ôté de u 17^0913 (le Lo- 
garithme de 15 , ) le refte o. 574031} eft le Logarithme 
•^« 3| ou 3^. 

* Vous voyesJ donc icy que les fr,aéî;ipns décimales, 
tant en Tufagc des Logarithmes qu'en l'ufage des nom- 
bres vulgaires , donnent une grande facilité : & par- 
taqt ^ous les recommandons pardeflus tous les autres* 

Pour trouver le Logarithme d'un nombre rompu , 
il faut ôter le Logarithme du Numérateur du Loga- 
rithme du Dénominateur, le refte eft le Logarithme 
«quis , en luy ajoutant la marque - , qui fignifie moins. 
^ Mais ,^ il faut ^fçavoir qu'on doit opérer autrement 
par Logarithmes des Nombres rompus que par Loga- 
rithmes des Nombres entiers , ou d'entiers avec fra- 
«âions > œ^ que nous n'enfeignerons pas. icy , parce 
que rarement ils viennent en ilfaige dans les refolu- 
tions des Triangles. Ceux qui le défirent fçavoir , le 
pourront apprendre en l'' Arithmétique Logarithmeti- 
que d'Henry Briggs yQVi le fondement & l'excellent 
ufage des Logarithmes aux qiieftions Arithmétiques 
^ Géométriques font am|>lement déclarez^ 

Ai» 



$ Chàp. I. Z)^ Vufa^edi cês TaJkUu 

Trouver le nombre à* nit Logarithme donné. i 

Cherchez en la deÂiicrc Table entre les Logarick- 
mes de iQoo & 10000 , ( ians avoic égard à Taprc^ 
miere figure ,J le Logarithme donné , & re^iarque? 
^C5 deux choies. 

Premièrement, fi vous trouve» ex^ftement le Lo- 
garichme donné , vous y avez vis à vis le nombre re« 
quis ; Et fi la première figure du Logarithme donne 
eft moindre que 5 , coupez du nombre trouyé vers I4 
droite autant défigures quelle tft moindre , le reftc 
fera le nqmbre entier requis , & les figures coupées 
feront des fraâions décimales. Mais , h la première 
figure efl plus grande que j , augmente* le nombre 
trouvé d'autant de zéro qu elle cft plus grande. Ainû 
\t Logarithme 3. 55130}! étant proppfé , fon nombre 
fera ^6jx fi %. 5515051, fon Nombre fera i^û-^iQ. 
ï.55Zjojt , fon nombre fera )St|^> fi o. 55i50}x foa 
nombre fera 7^; fi 4. 55150}!, fon nombre fera 
15(^70: fi' 5. j5i}o3i » fon nombre fera jjiîyoo. Ainfi 
des autres. 

Secondement y fi on ne trouve pas exa<P:ttiient le 
Logarithme donné , & qu'on demande plus de qua« 
tre figures , faites ainfi. 

I. Cherchez comme auparavant , fans avoir égard 
à la première figure , le Logarithme prochainement 
moindre que le donne , & prenez le nombre répon-? 
dant au Logarithnae trouvé poiu: les quatre premières 
figures du nombre requis. 

z. Otez le Logarithme t?rouvé du Logarithme don-* 
t)é , & augmentez le refte dHm, deux, ou trois zéro ^ 
félon le nombre des figures que vous demanderez qut 
|re les quatre trouvées. 

}. Divifcz ce refte ainfi augmenté par la dififerençç 
entre le Logarithme trouvé & celuy qui le fuit inv- 
mediatement , & mettez le quotient vers la droite 
des quatre trouvées, Cela &it , regardez la première 



C H A p. I. Vo Vftfageâc ce$ TaliUs^. jr 
fipmbce entier & la &aâ:ion du nombre trouvé , cptnr 
fne nous avons dit auparavant* 

Exemple. Qu'il faille trouver le npmbre répondant 
âu Logarithme donné 4, 55x4118. 

Le Logarithme qui fe trouve en la Table entre 
ceux de 1000, Se ioooo> fans avoir égard ila prer 
xniere figure , approchant le plus prés & moindre que 
le donné, eA |. 552;o;i » duquel le nombre çft }5<^7, 
qui (ont les quatre premières figures du nombre re- 
ijuis. Or ce Logarithme trouvé étant pté du donné > 
le refte cft 10S7 , que vous augmenterez de trois zcroj 
pour avoir 1087000, Divifez ^ ecy par 1^17 » la ditfc- 
içnce entre le Logarithme trouvé & le fuivam» Iç 
quotient cft 894 : mettez ces figures après 3567 » 6ç 
vous aurez le nombre ;5^78$4* Or puifque la pre- 
mière figure du Logarithme donné eft 4 > le nombre 
cequis cft 35^787!^ • 

Trouver U Racine ^^Marr^e êu Cubique d'un. 
nombre donné. 

Bien quemon intention ne (bit que de brièvement 
décrire en ce lieu la manière de>fupputec les Trian- 
gles : Toutcsfois puifque Tufage des Logarithmes cft 
admirable aux extrairions de Racines Carrées > Cu- 
bique*, &c. j'ay trouvé bon d'y ajouter en peu de 
irgnes , comment on les peut tres-facilemcnt cxtrairç. 
four avoir la racine quarrée d*un nombre donné y fn^ 

nez* la moitié du Logarithme du nombre donné ^ 

UqneUe fera le Logarithme de U r4cim qnarrée 

quon demande. 

Comme fi on demande la Racine quarrée de U57 : 
Ion Logarithme cft j, 05)93355, &b moitié 1.549^67$, 
qui eft le Logarithme de 35-^^ la Racine Quarrécrô- 
quife. 
pour trouver la Racine Cubique ttun nombre proposé , 

le tiers du Logarithme du nombre donné fera le 

Logarithme de lafiacine Cubique qu*on demanda. 

Par exemple on demande Ja Racine Cubique ^c 



s Ch.Ap. I. DeTnfagc de ces 'fahles: 
Ï2570. Son Logarithme eft 4. 0993355 , & fc tiers 
i. 3^<>445i , .qui eft le Logarithme de i^-^ la Racine 
Cubique rcquife. 
De la ndtHre,cr de U atnfiruWen des Logarithmes. ^ 
Les Logarithmes font des nombres pris à difcre- 
tion » lefquels étans joints ou corrcfpondans à des 
nombres Géométriquement proportionels retiennent 
toujours entte eux des différences égales , ou bien 
qui girdcnt la progreffion Arithmétique , tandis que 
ceux defquels ils font dits Logarithmes , çonferveat 
ta Géométrique. 

Voyez la premicre colomne de- 
cette Table, ou (ont les nombres Géo- 
métriquement proportionels , auf-' 
quels il repond vis à vis dans les aiu 
1res coldmnes leurs Logarithtties , qui 
pciivejQt eftce pris à dilcretion , com- 
me vous voyez, ctâni Ubre de pofcr 
ce que, Ton veut pour premier Loga- 
nrîthme , & pour leur différence proy 
greffive. Mais , ayant détermine le 
logarithme de deux nombres , il n'eft 

Îlus libre d'en déterminer d'autres.- 
ar exemple le Logarithme de l'unité étant i , & rfe 2, , 
•étant 2 , le Logarithme de 4 fera par ncceffitc j 5 & 4 

fera le Logarithme de 8. Que fi le Logarithme de Tti- 
'nitc eft j , &le Logarithme de 2 eft 5 , le Logarithme 

de 4 fera ncccffaircment 7, & y fera le Logarithme 

de 8, ,Aiafi des autres. . . 
" " Or Jâ propriété des Logarithmes eft telle ^ qiio 
• quand qtiatre nombres font piroportionels 5 la fom- 
"me dcletïrs Loearithmës extrêmes eft égale âlafom* 

jme des Lpgarithmes moyens. 
\- Exemple. Comme x eft â8, ainfi \é eft a ^4 U 

fomme du Logarithme dé 2, & du Logarithme de 

64 , fera égale à la fomme des Logarithmes de 8. 5c 
'de 16. ' . - 



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^4 


7 




60 


1x8 


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70 


156 


9 




80 


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10 




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1014 


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100 



Chàp. I. De Tufage de cesTabîesZ 9 

D*où il fait qu'au lieu de faite la Règle de trois 
car mulciplicarion & par divifion , pour trouver com- 
«ne a l'ordinaire le quatrième noipbre proportionnel » 
il oh'ajoûteles Logarithmes des moyens, &que de 
teur fommc on ôte le Logarithme du premier , il re- 
liera le Logarithme du quatrième requis » à côt^ du- 
<5ucl on trouvera ce quatrième nombre. 

Et partant il n'y a qu'à faire éts Tables des Lo- 
garithmes cotrefpondans à tous les nombres naturels > 
comme je montreray cy-aprés. Je dis correfpondans 
depuis Tunité confecutivement fans laiflTer de vuide , 
comme il y a entre les nombres cy-deflus propor- 
tionels 4. 8. i(i.&c. où les nombres 3. 5. 7. ^•&d 
manquent , qui pourtant doivent avoir leurs Logarith- 
mes, parce qu'on en peut avoir befoin. C'cft pour- 
quoy, il faut faire la diflfercnce de* ces Logarithmes 
fi grande , qu'on puifle aisémeiic aflignet a chaque 
nombre Ton Logarithme » fans 
que les &aâions en puifTenc être 
fenfibleis , comme il fera dit. 

Pour cette 6n l'on a fuppofé 

pour plus grande facilite que le 

5. 0000000 j Logarithme de i.fut o. & que le 

4.oQooooo| j^^ j^j^j^ç de 10 fut 1.0000000, 

f.oooooopi o , . , j - ' 

^.0000000 .q^ic le Logarithme de 100 ftit 
7.0000000 i.ooooooo, que celuy de 1000 
8.0006000 Ifuf 3.0600000, & ainfienfiiite. 



Prop. 



Lêgarith^ 
mes. 



I 

10 

ipo 

1000 

lOOOO 

lOOOOO 

I 000000 

I 0000000 

I 00000000 



0.0000000 
1 .0000000 
1. 0000000; 



comme vous voyez en cette Table, Où il eft à rc- 
marque^r que la première figure du Logarithme , nom- 
mée c^dinaircmcnt CaraEierifiique , eft toujours moin* 
die^d'une unité que les ifigurcs dont le nombre natu« 
rcl eft compofé. Si par exemple il eft de S chif&es » 
la première figure de fbn Logarithme fera 7. Si de ii 
chiffres , fon Logarithme aura^ 11 pour CaraOerifii^ 

Et fur ce pied & fondement on a trouve les Lo- 
gariihipcç de tous les nombres, même, de ceux qui 



^t4ei9>iO><leipâioP9ckioo âiooo, &c âbnt 
pîi a drclTE des Tables > fi bien qu au lieu d opérer 
par timtciplicatiop & par divifiou pour trouver le 4» 
jBQipbre requis , fi Ion opère par Addition & par 
$oil^ra£Hon des Logarithmes qui répondent aux uois 
iioi:9t>res donnez > on aura le Logarithme do 4. tt^ 
quisy dcôté duquel il fe trouvera en la colomne det 
jDofnbres naturels. 

Et doutant qu'avec les Tables des Sinus te des 
Ts^^ntes y comme étans des ao^ibrcs naturels » il 
laut Qperer pv muldplication & par divifion > on a 
wflî cherché \t% Logatithmef de tous ces nombres 
^ Sinus le Tangentes k Tég^d du Sinus total 
locpooooooo , auquel on applique pour fon Logarith- 
me lo.oocooop » & tous ies autres k proportion , que 
Ton a fubftituéen la place d^% Sinus & desTangeiw 
tfft ordinaires. 

Pe façon qu au lieu de les multiplier & delesdi* 
Yii^ s'ils y éa>ienc , on ne fait qu'ajouter & fouftrai-^ 
re leurs Logarithmes ^ pour avoir le 4. requis , à coté 
duquel on trouver le degré Çc minute , comme fi c'é- 
|o>t le Sinus ou^Ia Tangente m&me > puisqu'ils font 
iubftituez en leur place. 

PoHr tr^mjer h Ij9gêrUbme d'un nombre donné 
quel qH'ilfin , comme pdr exemple de 9 , nui efi entre 
jt tà' i^ > dont les Logarithmes font dé je donne^yffd^ 

voir o.ooooooQ, ^ i. ooooopQ, ou tien 0.00000000» 

0' !• ©oooçoop , en les augmentant d'un 7(ero , four 

trouver plus exdSemtnt le Logarithme f faites en 

cette forte. 

Entre » & 10 augn^entesç 

d^âutanç de ^eiro que le Lo^- 

garirhme de lo & des au- 

frcs proportionnels % ^pm- 

mc icy de fcpr j pour avoir 

l^xaAenient dans le même 

nombre de figures le Lo- 



f report. \ LogMtth. 



1 .oooocpo jo.ooooooco 

3.1^1x777 jo.jooooooo 

I o.coôoooo 1 1 .00000000 



►oji 



1 0.0060000 i I^OOCOOOOO 
j.6i34i|i|o.7joooooo 
5 . 1 <;iz777 lo./ODOooo© 



Chaf. ï. JieVnfuge 
earithtne requis , fçavoir cp- 
tre les nombres A » B , ti ou- 
vez un moyen Géométrique 
proportionnel C ; lequel é- 
uc moindre que 9.0000000, 
il faudra chercher encre le 
nioindre C , & le pins grand 
jB un autre moyen propoi:* 
cionnel D , qui eft encore 
înoindre que 9. oeooôQp , 
ç'eft pourquoy entre le 
fnoindre D & le plus grand ---^ 
B on cherchera un autre 
inoyen proportionnel E > en- 
tre lequel & le plus grand 
B on trouvera un quatcié- 
ine moyen proportionnel F 
qui eft icy encore moindre 
que 9.0000000 9 c'eft pour 
quoy il faudra trouver entre 
Je moindre F , & le plus 
grand B , un dnquicme 
moyen proportionnel G, qui 
fera icy plus grand que 
9. 0000000, ainfi entre le 
plus grand G , & le prochai- 
nement moindre F , on cher 
cher^ un fîxiéme moyen 
proportionnel H » qui fera 
maintenant moindre quç 
9, 0000000: c^eftpourqupy 
çnae ce moindre H> ii le 
prochainement plus grand 
G, oin trouvera un feptiéme 
ipioycn proportionnel (, qui 
eft bien plus grand que 
jp. QçoQooo , |!na|s nop pw 



JéCf^Tahlcf^. 



G 
H 
F 

"g 

I 
H 

T 
K 

H 

1k 

L 
H 

L 
M 

H 

L 

N 
M 

N 
O 
M 

O 

P 

IM 



Pr$fart. 



lo.ooopooo 

7.458^411 



lo.ooooopo 
70^f4*ï 



10.0000000 
^.jo/7104 

8.^j^tf45i 
^.}o;7i04 



J?.JPJ7104 
5.13^8170 

8.57^8713 



^.X55«i70 
'9'0S79777 
8.^7^8713 



9'0S79777 
5.0I7J333 

8.^7^8713 



90173$}$ 
^-9970796 
8-57^8713 



5>.oi73333 
^.0071008 
i'997079^ 



^.0071008 
^.001x388 
Z.997079^ 



^.0011388 
8.9^5^088 
8 9^970796 



LâgWt. 



1. 00000000 
o.tt7/ocooo 
0.7/000000 



1 .00000000 
0-^37/0000 
0.87/00000 



1 .00000000 
0.^^87/000 
0-^37/0000 



0.^^87/000 
0.^/311/00 
o-^J 7/0000 



0.^687/000 
o.^éo^37/o 
o.^3^ift/oo 



0.^^0557/0 
0.5/70311/ 

0.5/3 Il/OQ 



0.5/70311/ 

0.5//07811 
0.5/3I1/OQ 



o.5/;o78ii 
o.5/4ioi/<î 
0.5/3 ii/oç 



0.5//07811 

0.5/4/8584 
0.5/4101/^ 



0.5/4/8584^ 
0.5/434/70 
0.5/4101/6 



0.5/4)4/70 

0.5/4113^3 
05/4101/6 



[ Vrafort, 



^.0011588 
5.00087J7 
8.^5^5^088 



5.0008757 
5.0C014XZ 



5-000141 ^ 
^'9999tSO 
8.555^088 



5.0001412 
5.0000851 
^9999iSO 



5.0000851 
5.0000041 
S.9999^SO 



il CnxvA. De fufage de ces Tahles. 
avec an fi grand exçcz com- 
me le précèdent G. Ainfi 
en cherchant entre le pro- 
chainement moindre & le 
prochainement plus grand , 
des moyens Géométriques 
proportionnels , on aura àzs 
nombres qui approcheront 
toujours de plus en plus du 
nombre propofé 9.0000000, 
lequel enfin fe renconttera 
icy le x6> moyen proportion- 
nel : Après quoy il fera fe- 
cile de venir à la connoiflan- 
ce de (on Logarithme; car 
comme entre les nombres 
A , B , nous avons trouvé un 
inoyen Géométrique pro- 

Ïonionnel C » (i ent^e leurs 
►ogarithmcs on trouve un 
moyen Arithmétique pro- 
portionnel , ccluy-cy fera le 
Logarithme du premier 
moyen Géométrique pro 
portionncl C. Ceft de cette 
manière qu'on trouvera les 
Logarithmes de tous les au- 
tres moyens Géométriques 
proportionnels , & par 
comcqucnt du dernier 
9. 0000000 9 ou du nom- 
bre pioposé 9 , (Ravoir 
o. 9y^i^i$o. 

On ne trouvera pas au- 
tr îment les Logarithmes desj bB 
D >mbres premiers , & pàrl& 
l'addition de leurs Logarith- 



o 

Q. 

p 

a 

R 
P 

R 
S 

P 

R 
T 
S 

T 
V 
J 

V 
X 

s 

V 
Y 
X 

V 
Z 

Y 

V 
Se 
Z 

V 

AA 

& 

AA 



50000041 
^'9999^10 
^'9999^5^ 



5.0000041 

8.5^5584; 
^'99996S0 



5.0000041 
^-99999^} 
^'9999^^5 



Logartf. 



<"-^/434;70 
0.5/4184^7 
o.5;4î'iî^3 



0.5/418467 
0.5/41/41/ 
0.5/4123^3 



0.5/41/41/ 
0.5/413885 
0.5/411363 



0.5/41/41/^ 
0.5/4146/1 
0.5/413885 



0.5/4146/ 1 
0.5/41417» 
0.5/413885 



0.5/41417Ï 
0.5/414080 

0.5/413885 



0.51414171 

0.5/414117 
0,5/414080 



0.5/42417Ï 
0.5/414113 
0.5/414117 



5.0000041 
%.999999^ 
^'99999^1 



5.0000041 
5.OcrO00lé 

%.999999^ 



5.0000016 
5.0000004 
8.5599^^1 



0.5/414171 
0.5/414147 
0.5/414111 



0.5/414171 
0.5/4141/5 

0.5/414147 



0.8/4141/5^ 
0.5/4141/3 
0.5/414147 



C il îK. 1 1 Des Tritmgh nttH. nBan^. 
tncs on aura facilement les— 



n 



BB 

GC 

& 

BB 
1>Ï> 



Profort. \ Log^rk, 



10.5 



5.1000004 10.^/4 141/ 3 



^'999999^ 
%.999999t 



5.0000004 
5.0000000 
Z.999999^ 



0.5/4141JÛ 
o.9S^HM7 



Logarithmes des autreis nô- 

bres > ce qui eft fi évident 

par ce que nous avons die 

cy-delTus , que ) ay honte 

d'en padtc davantage. Je 

fçay Dien pluâeurs autres 

Méthodes pour rinvention\ £S 

des Logarithmes , mais je n'en ^ay point de plui 

prompte que celle-cy. 



0^/4143^/5 
0.5/414»/! 
0.5/4141/0 



CH AP ITRÈ IL 

Du CaIchI des Triangles nâtlignes refhingles* 

Ôb sbryations. 

t. *rx Es Triangles reâangles , tanc reétilignes qde 
JLx Spheriqiles , les cotez comprenans Tangle 
droit font appeliez jambes , & le côté qui luy eft 
oppofc, hj/fotenufe. 

2. De tout Triangle tant reftiliene que Sphetique, 
le plus grand angle eft.foûtenu du plus grand coti» 
Et le plus grand côté foûtient le plus grand angle. 

3. De tout Triangle reéliligne les trois angles pris 
cnfemble font égaux à deux droits. 

. 4* Aux proportions fuivàntes eeneralementnoils 
avons obfervé un tel ordre» que les premières (ont 
pour trouver les Angles , & les dernières pour'leç 
cotez. Et de ccux-cy aux Triangles te ftangles, prc*- 
mierement les jambes, 6c puis après Thypotenufe. 

5. Les termes connus, tant angles que cotez , ,fe- 
iront marquez d'une petite ligne, & les termes requis j 
ii un petit cercle, ou , comme Ton peut voir icy. 



'ig Ça A p. IL I)esTria9^.rc£Ht.reii4n£h 

y L P R o Pr Lîûti^ connus les angles , & Une jambe v 
trouver rhypotenufc. 

Comme J^ Sinus total , V ^ / 

ui ia jamhe\ conntu ; \ ( connue , 

jiinfila Sécante de V angle aigu adjacent f la jambe 
A rhypotenHfe. 

Si quelqu'un veut concoure le Logarithme de la 
Sécante d'un arc , on le trouvera eh ôcant le Loea« 
rithme du Sinus de Ton complément , du Logarithme 
doublé du Sinus total : le ^efte fera le Logarithme re- 
quis. . . - 

Ainfi étant 9. 9445811 le Logarithme du Sinus de 
Çi 'd..46. dç 2^0.' 0000000 i il irefte 10. 0554173 U Loga-*' 
lichme de U Sécante de iSjd.iô. 

Autrement éias Sécantes. 
% . • .■ t. - . . . ' ■ ' 

Comme le Sint^ ieVangU. offoséà la jambe connue t 
" ui la Jamb'i connue : . 

'Ainfi le Sinus total, 

A Vhjfotenufé. ' ^ ' - 

V I L P R o p. Etans connues les jambes 9 trouves 

l'hypotenufc. . . 
I . - - - 

09erchex» premièrement les angles par la u Prop. cJ* 
fuis après ihjpotenufef par la précédente C. Prop. ' - 



CHAPITRE IIL 

De la fiippuiation des^ Triangles reElilignes 
' " obliquangles. 

L Pjlop. TjTans connus deux cotez , &un angle op- 
JlI pps^ i l'un des deux , trouver l'angle op- 
posé a l'autre : Moyennant quonffache s'il eft aigu oh 
obtus* * . Comm9 



^ k À p. 1 1 1. Des Triangl. rtttiU phli^^ ij 
^ C^mme le cité êffùsé à l'angU connu i 
ji$$ SinHs du même éngte i 
Jlinfi l'autre cité 9 \ 

Au Sinus de tungte opfosi l ce citi. 

ÏU JP R o i^. Ecanifi connus deux totex , & rahdê qû'ill 
comprenaent » trouvée les autres angles; 

Comme lafimmo des cêtex, connus , 

A la différence dis mêmes côtel ; ; ' 
Ainfi la Tangente delà moitié de la fimme disan-^ 
gies inconnâs , 
A la "tangente de la moitié de ledr différencia 
Partant (i à la moitié des angles inconnus » qui (ont 
le complément de l'angle connu ï i8o degrez , la dif- 
férence trouvée éft ajoutée > la fditinie Teira le plusf 
grand angle > & fi tlle en eft 6tée i le tefte fera le 
xrioindf e ângic; 

It 1. 1* id p^ Etaiis cbntiui lei tft>is ràtez » trduvef 
quelcp'un des angles. 

Prêtiez le plus girahd coté|>our la bafe , far laquîclA. 
le tômbç de Van^é'>çpposé une perpendiculaire > ré-^ 
duifaat le Triangle fen deux Triangles itOaA^ési. 
Alors on dira i"^ ' 

tomme la Bafi , 
- - A la fomme des autres chez, i 

Ainfi ta différend des tèêmes cttei , 
/ A la diffeiren ce des deuxfigmehs de la tdfe^ 

la différence trpuvée étaiit ôtée de la bafe » ta pef-' 
pèndiculaire divife le fefte en deui p'arties égalés; 
Ainfi donc aux deux 'triangles reâangîes rEypote-^ 
nufe eft connue atec une ïambe , par lerqùellcs on 
treuve les angles par la IL Prdp. dû CKap. II. 






i8 C H A p. n i. Hes trrangi rcBit. eiUf. 



Exemple. Au triangle obli- 

quanglcÂBC, fontcoti»- 

nus AC 1177, AB 8^5 g 

& BC 6ji : on deman-> 

.de quclqaun des angles. 




Comme A C 

iABtBC 
ÂinfiAB-BC 



1177 -- 
145)7 -« 



Logarithmes. 

- 5. 1061909 

- 5.1751118 

5-3445777 

- i-4î^J^68 



 AD 17^ 

REMARQUE. 



> Vj- 



0» fei$l: 0i»gi trouver le Logarithme dn quMriinii 
mnésev requis ^ file câmplen^ne ^rithnctiijue ^ufre-^ 
mier Logarithme , que Von a en Votant de 10. oQpçc^oô, 
efi" ajouté aux deux autres , & que de iafomme on 
60f 'Vtrf . iug4fH^ :h fr€mkr< /sf^.^\ C^^^^.^f^ 
VexemfU précédante ■;• 
Logarithmes, 
AC I277ii,h3^i 

ABtBC I4p7-Î'ï7i5i«i8 
AB-BC A5r.i>3g 7?559 

AD 273- 12-45^3868 - - - 

5i un Logarithme propcfé né peut pas êtrefonftrait 
de To. 0000060 , comme ceux des Tangentes des arcs 
outre J^^ degrez, , il le faut fonfiraircde io.ooôoooo ^ 
t^ faire comme devant, jiinfi le complément Arith^ 
nutique du Logarithme de la Tangente de 66 degrez. , 
1^ 9. 6 4 8 5 8 5 1 , qui efi aujji le Logarithme delà Tan- 
gente de fin complément* 

Or AD 17} étant ôté de A C l'i 7 7 , il demeure 
D C 1004 % dont la moitié 501 eft C E ou E D. Main- 




tenant au Triangle reâangle A B E eft connue l'hy?- 
i>otenafe A B 8 6 5 , & la j^mbe A E 775 > par lefqueù- 
Ics on trouvera l'angle A B E «^3 d: 38 & Tanglc 
B A E 2(î d: ti\ De même au Tnandexcâangle C B E^ 
cft Thypotenufc G B *ji , & la jambe C E 502 , par lef- 
qucllcs on trouvera Tapgle C BE 5^ d: 35'. ftianglf 
B G E 37 d: 15'. Si vous ajoûtci l'angle CBE ci d: 3$'; 
à l'angle A B E £3 d: 38'. la fdnime eft l'angle A B â 
ii^diy'. 

ÂutHemènt. 

Ajoutez énfi:fnt)le les trois cotez» & de la moitié 
de leur fbmmé {buftrayez chaque côté comprenant 
l'angle requis , pour avoir Icûts différences. Apréâ 
tela faites ces deux analogies 9 
I. Corne qnelqH'Hn des citez, C9i»f venant V angle refuisj 
A ûuel^m'nne des différences troûvfes j 

Ainfi Vautre diffetehce, 

A un quatrième nombre^ 
i. Comme Vautre cet/ cùmf tenant Van^ reigùis^ 

Au Stnus toial^ 
^ ,AinJî le^ quatriîfne nombre trofsvf $ 

À unfeftiémei . . v 

Ce feptiéme nombre étant multiplié pir le Sinùi 
total, la tacine quarrée du produit fer^ le Sinus de là 
mditié de l'angle requis* 

Ou plus facilement par togarithmeé ,; ajput^ le 
Logaritnme du iinus total au feptiéme Logarithme s 
la moitié de la fomme fera le Logarithme du Sin^ç dé 
la moitié de l'angle requis. . . ^ 

Exemple* Au Triangle précèdent foit requis Vtà&^ 

rkC iiii 

Lescptci^AB 8^5 

CBC éji 

La fomme des cotez 2774 * 
La moitié de la fomme 1387 

B i/ 



to C H A P. I II. Des TridH^. feBil. ohli^. 

La différence de A B ^ 5 2. i le Log. a. 71 ytf yay 

ta différence de B C 7 5 5 le Log. 2. 8 77 9 4^^ 

la {brome 5* 5 9 5 ^ 1 7 4 
te Logarithme de AB . %6^ 2. 9 J 7 o 1 6 1 

Le Log: du 4. avec le Lôg. <îu Sin. total 12. ^ 5 8 <î o i j 
Le Logarithme de B C 632 2.8oo>i7i 

Le tog. du 7. avcd le Log. du Sin. total 19-8578842 
La moitié eft le Log. du Sin. de 58 d: (5^ 9. 9 2 8 9 4 2 1 
Son double 177 d: 13'. eft l'angle requis ABC. 

Ou bien ajoutez les complcmens Arithmétiques 
des Logarithmes des cotez c«nprcnans l'angle leqiuis , 
:aax Logatithtnes àes différences trompées , la moitié 
de lafommc ftrj^ le Logarithme du Sinus delamoi^ 
dé de Tangle requis. Comme au même exemple. 
Logarithmes. 
Les cotez r^ ^ * ^ 5 7-0^20839 compl. Arithm. 
- t-B C ^32 7.1 992829 compl. AtiihmT 
La diffct. de A B 5 2 2 2. 7 1 7 6 7 o 5 
La di|fer. de B G 7 5 5 2, 87794^9 • 

La morne de la foimne 9-9289421 comme aup^a- 



vant. 



V- ' * ' .... 

r IV. P Bi^op. Etans conntfs les angles & un côté, 
tibuver quelqu'un des autres cotez. 

• Comme It Sinus de Vdngle cfffùfé a» cS^é connu , 

Auedté C0nnu, 

• Ain^le Sinus de Vangle opfojï aucêtfrequify 

Au dté requis. 

V. P R OP. Etant connus deux cotez , & l'angle qu'ils 
comprennent , treuvetle troifiémc côté. 
Trouvez, frcmieremtnt les autres angles far la 2. 
Trof. de ce Chapitre , c^ p^s apr/s le côté requis par 
la précédente 4. Prop. . 



I w 



/ 



i *• i 



C A f • I y. Des TriMg. Sfben rcQung. u 

y *- x, ' , I I I I I I ■ I I II <! I 

CHAPITRE IV. 

Dh calcul des Triangles Spheriques reCtangles. 

Observations. 
f« Q I une des jambes eft Quadrant , l'angle oppofé 
i3 â cette jambe fera droit ; fi moindre que le Qusu 
dranc » aigu ; Se fi plus grande , obtus : ^ au conttaire. 

2. Si une des jambes eft quadrant > l'hypoteRufe fera 
auffî quadrant: mais, fl l'une & l'autre (ont moindres 
ou plus grandes que le quadrant , l'hypotenufe fen 
moindre' que le quadrant : & fi une eft plus grande que 
le quadrant * & l'autre moindre , l'hypotenuTe /era 
plus grande que le quadrant -, & au contraire. 

}. Si un des angles touchans Thypotenufe eft droit » 
l'hypotenufe fera quadrant ; mais , fi ^chacun eft moin- 
dre ou plus grand qu'un droit > l'hypotenufe fera moin- 
dre que le quadrant : & & l'un eft plus grand qu'un 
droit y Se l'autre moindre , l'hypotenufe ftrà plus g]ran- 
do que le qiiadrant : & au contraire. 

4. De tout Triangle jSphcrique lc$ trois angksibnt 
plus graads que deux droits^ 

I« ,P ^ Q p. Etant connu un angle oblique , Su tyy 

jambis ^djgçepi:eicet angle, trouver l'^uti^e 

aiigte oblique. 

Comme le Sinus total , 

^n Sinus de l^ngle pilique connu § 
^inj! le Sinus du comfletpient de U jambe connue 9 

Au Sinus du complément de V angle requis. 

n* Prop* Etant connue une jambe , & un angle 
oblique oppofé d cette jambe , trouver l'autre an- 
gle oblique : Moyennant qu'on fçache s'il efi aigu 
!0U obtus : ou bien fi l'hypotenufe , ou Vautre jambe » 
Ci? ^9'^^^^ ou plus grande que le quadrant. 



|i € If A 9. Vf. Des Jriangh Spherif. reâ. • 
Comme le Sinus du complément de lajamhe connni^ 

An Sinns 4f^ complément de V angle coi^nn ; 
■ jiinji le Sinus total , 

uiu Sinus de V angle requis. 

Autrement. 

Comme le Sinus total , 

jiU Sécante de la J4mhe connue, 
jiinfi le Sinus du complément de l* angle connu 9 

Au Sinus de l'angle requis* 

1 1 L F n o p. Efranc connue rhypotenufc , & une jat^ 
be» trouver l'angle oppofé à ccçce jambe. 

Comme le Sinus de l'hypotenufi , 

Au Sinus total 3 
Ainfi U Sinus de' la janAe connue ^ 

Au Sinns. de l'angle requis. 

Autrement. 

Comme le Sinus total, 

A la Sécante du complément de Phjfpotâuuji | 
Ainfi le Sinus de la jambe connue , 

Au Sinus de l'angle requis* 

|V. Prop. Etant connues les janabes , trouver le^» 
quel on voudra des angles obliques. 

Comme le Sinus total. 

Au Sinus de la jambe adjacente k l'angle requis*. 
Ainfi la Tangente du complément de l'autre jambe , 

Al la Tangente du complément de l'aygle requis. 

y. P RQ p. Etant connue Thypotcnufc & une jambç , 
trouver Tangle qu'elles comprennent. 

Comme le Sinus total , 

A l^ Tangente du complément de l'hjfpotenufe y 
^infi la Tangente de la jambe connue , 

jiu Sinus dfU complément de i'angle requis* 



C H A p. I V. Des Tri4f0gL Sfheriq. reS. ij 

VI* P^o p. Etant connue rhypotenufc, & unaiïglc 
oblique , trouver l'autre angle oblique. 

Comfnt le Sinus totale 

A*s Sinus du consplemeut de l'hyfotenufi s 
Ainfi la Tangente de l* angle Mique connu , 

A la Tangente du comblement de l'angle re^iSé 

V 1 1. P R o P. Etant connue Thypotcnufe , & un angle 
oblique, trouver la jambe opppsée à cet ^mglc. 

Comme lé Sinus total y 

Au Sinus de rhypotenufi -, 
Ainfi le Sinus de l* angle oblfi/ue connu , 

A^ Sinus de la jambe requife. 

VIIL Prop. Etant connue Thypotcnufe » & une 
jambe , trouver Tautie |ambe« 

Comme le Sinus du complément de la jambe connue 9 
Au Sinus du complément de l*hypoteuufe , 

A^^fi le Sinus total , 

At^ Sinus du complément de la jambe requife. 

' AVLtKEHnVJ. 

Comme le Sinus total , 

A la Sécante de la jambe connue : , 

'Ainjî Le Sinus du complément de Vhypotenufe , 
Au Sinus du complément de la jambe requife. 

IX. P R o p. Etans connus les angles , trouver laquelle 
on voudra des jambes. 

Comme le Sinus de V angle oblique adjacent k la 
^ jambe requife , 
Au Sinus du complément de Vautre angle obliques 
Ainfi le Sinus total , 
A» Sinus du complément de la jambe requife. 
Autrement. 
Comme le SinUs total» 

A la Secaiite du complément de V angle oblique 
adjacent à la jambe requife , 

B iiij 



%^ C H À p. f V. Des TriângL Spherif. re&. 
^infile Sinms du complem. de VâHtre dngle okli^Ui f 
Ah Sinjadu cemplepunt de léf jambe retjuifié, 

X. P R o p. Etant connue une jambe » 9c unang|e 

oblique adjacent à cette jambe ^ trQUVçc 
( i'atttre janipef 

Coff^me le Sinus tetal , 

Au Sinus de la jambe cennuêy 
Aiujî la Tangente de l'angle ebli^ue cenuu « 
^ la Tangente de la jambe requife. 

Kl. P R o p. Etant connue une jambe , ic un angle obli^ 
que oppofé i cette jambe , trouver l'autre jambe s 
Moyennant qu'enfçachefi eUe y ou bien l'hyporenu* 

' S^y efi moindre OU plus grande que le quadxa^tiom 
fi l'autre angle obliquf efiaig^AU ^btus. - 

Cpmme le Sinus totale 

A la Tangente du complément de V angle oblifUê 
connus 
Ainfi la Tangente de la jambe conpi^e^ 

Au Sinus de la jambe requifi. 

JCII. P R o p. Etaqt connue Thypotenufe , & pn angle 
oblique, trQUver (a jambe adjacente ^ cet angle. 

Comme le Sinus tot^l j. 
Au Sinffs du con^plemfnt de V angle fbli^ue c^nnpp 

Ainfi la Tangente de (*hypotenufe , 
A la X^ngente de la jambe requifi. 

XIII. P R o p. Etans connus les angles ^^ 
trouver l'hypotcuufc. 

Çpmme le Sinus totale 

A la Tangente du complément de l'un des a»^ 
gles obliques i 
^.inftlaTangente du compL de Vautre angle obliqu^ 

^u Sinus du complément de fhyjftenuji. 



p 

I 



Chj^p.IV. Des TriângU Sfheriq. reÙ. îj 

K i V. P K Q Pf Etans connues les jambes » Cf pnyer 
Vhypotenufcf 

Comme le Sinus total f 

Ah Sinus du comblement iune JesjéUÊ$tes / 
jlinji le Sinus du complément de l'OtUtre jambe » 

Au Sinus du complément de Vhjfotenuje. 

XV. P n o p. Ectiit connue une janabe s & un angle 
oblique oppofc à.çecre jambe , trouver l'hypocc- 
nufe : Moyennant qu'on /fâche Ji elle , ou Vautra 
jambe , efi moindre ou plus grand que le quadrant « 
ifu fi l'autre angle oblique èfi aigu qu obtus. 

Comme le Sinus de l'angle oblique connu ^ 

Au Sinus de la jambe connue ^ 
Ainfi le Siffus total , 

Au Sinus de Vhjpotenufi» 

AutR|!MENt« 

Comme le Sinus totale 

A la Sécante du compU de l'angle oblique connu i 
Ainfi le Sinus de la jambe connue , 

Au Sinus de l'hypotenufe. 

X V I. P R o p. Etant connue ime: jambe , & un angle 
oblique adjacent à cette jambe > trouver Thypotenufe^i 

Comme le Sinus total <, 

Au Sinus du compl. de V angle oblique connu : 
^infi la Tangente du compl. de la jambe connue ; 

A la Tangente du compl. de l'hypotenufi. 

CHAPITRE V. 
Du calcul des Triangles Spheriques obliquangUs. 

POur résoudre la plufpan des Triangles Spheriques 
obliquangies , on les réduit en deux Triangles re- . 
^angles , par une perpendiculaire y pree du bout do 



^ C R A p» Vi Des TrldHgl. Spheri^. ûhliij. 
cote connu ayant à Tàutte bout un angle connu > (ûr 
la bàfe , prolongée s'il eft neceffaire. Et alois 09 
trouve les termes requis par les termes connus des 
Triangles reâangles. Or puifque la manière par l'in« 
vemion de la perpendiculaite,qui demande trois ope- 
rations au moins , eft déjà vulgaire , & peut être faite 
par les Propoiîtions precedentesije n'en diray nK>t,pouc 
montrer comment on réfoudf a les Triangles fans l'in^ 
ventiôn de la perpendiculaire par le moyen de deux 
Propo(iti6ns feulement ; Et au lieu de pluificurs paro^ 
les qa il faut pour les exprimer , je le feray plus brie- 
vement par lettres. Ceux qui défirent en avoir les^dc-^ 
monflxations , les trouveront en \zTrU0n0nutrie Sri^ 
tanni^ue d* Henry Briggs* 

Pour ce faire fclon les Analogies fuivantes , mar* 
quez le Triangle propofépar les lettres A ^BjC, fça- 
voir langle duquel la perpendiculaire doit tomber par 
la lettre A , Tangle connu adjacent à un cocé connu 
par la Ictrre B , & le troifiéme angle par la lettre C ; 
fie où la petpendiculaite coupe la bafe à angles droits > 
mettez la lettre D. Les angles étant ainlî marquez, 
les cotez de chaque Triangle reâ:angle feront auffl 
marquez. 

Si les angles B & C , touchans la bafe B C , font 
aigus , la perpendiculaire tombera dans le Triangle ; 
il B eft obtus , elle tombera dehors ap dcU rangle^oh* 
tus C. 

Remar^He. 

Ptiis qu'il eft dit que la perpendiculaire doit tomber 
du bout d'un côté connu ayant un angle connu à l'au- 
tre bout , & que cela en quelque cas , comme de la 
|. 4. «9. & 11. Pfop, peut être fait en deux manières : 
partant en la 4. & 11. Prop, nous avertiront doù I^ 
perpendiculaire neceflairemcnt en cette rencontre doit 
tomber. Aux autrc$ deux il n'y a point de diiference. 



I. P R o p. Etant connus deux angles , 8c le c&tê 
d'cna'cux , trouver le troifiémc angle. 




» » eu 



1 

I. Comfke le Sinus tetat > 

Ah Sinus dû ccmfUment de A B 

V^/>r/?. Al Tangente, de ABC 

A la Tangente - du comblement de B A D 
Etant trouvé BAD Ton connoîtauffi CAD. 

%. Cçmme le Sinus de BAD 

Au Sinus de CAD 

^inj! le Sinus du cemflement de ABC 

Au Sinus du complément dç A C D 

Remarque. 
En la première & féconde figure , A C D eft le me- 
nie que A C B : mais en la troifiéirte , ayant trouvé 
A C D , il faut prendre (on complément à 180 degrez > 
polir avoir l'angle requis A C B. 

Pour montrer la facilité de calculer par ces analo- 
gies 9 je donneray un exemple , ^vec la plus bricvc 
manière d opérer. 

Soit du premier Triangle obliquangle BAC , connu 
l'angle B A C 104 deg. 6. l'angle A B C 38 deg. 6. & le 
irôtc A B 30 deg. 6. on demande l'angle A C B. 
I Logarith. 2 

Logarith. 
Si.co. p.8^5}ix 
Sin. 0.0818525 à.c. 
Sin. <,.87i(>4r4 

Si.CQ.ifj.Sjoôiijç 



AB jo d. 6. Sin. comp. 9.937530<S 
ABC 38 d ô. Taftgente 9.89x8098 



pAt5 55 d. 55'Tan.com.i9.8j03404 

CAD 48 d. 5' •. . • 

AB 44 d. 5e • • f , • • « « 



j»l C R A r • V. Der Triânfr. Sfheriq* Mifii 

IL P K o 9. Etans connus 4eu]( cotez , te i'anglc^ oppofé 
i l'un des deux > crouret l'angle qu'ils comprennent. 




ç*-ix 



I. Cpmme te Sinns utal , . , ^ 

A» Sinus du cùmfUment de A B 

Ai^nfi U Tangente de ABC 

A U Tangente dm cçmflementd^ B AD 

a. Comme U Tangente de A C 

A la Tangente de . AB 

Ainji le Sinns an complément de B A D 

. An Sinns dn complément de CAD 

Si la perpendiculaire tombe dans le Triangle, la fom« 
me de B A D , C A D ; fi dehors , leur difTereiiice eft 
l'angle BAC, qu on cherche, 

IIL P R o p. Etans connus deux angles , & le coté op-t: 
posé à Tun des deux trouver le troifiéme angle i 
Moyennant tjn* on fçache s'il efiaign on obtus : on 
hien <}ue Veffece du cètéoffoféà l'autre anj4e donnf 
foit connue^ 




I. Comme le Sinus f ot al ^ 

\4^ S^nns du çotnplçn^ptd^e 



AB 



CUÂT. V. Des Triânit.Sfheriq.bhliql ï| 

sAinJi la Tangente de ABC 

A ta Tangente du complément de B AD 

1. Comme le Sinus dn complément de ABC 

jin Sinus du complément de B C A 

Ainfi le Sinus de B A D 

Au Sinus de CAD 

Si la perpendiculaire tombe dans te Triangle > la 
fommc dcBAD,CAD:fi dehors , leur différence 
cft l'aiîgic requis BAC. 

IV. P R o p. Etant connus deux cotez , & Tangue qa*ik 
comprennent i trouver quelqu'un des autres atij^es. . 

En ce cas la perpendiculaire doit necelTaireoienc 
tombei: du côté oppofé à l'angle qu'on cherche* 




I) 

I. Comme le Sinus totale 

Au Sinus du complément de ABC 

Ainfi la Tangente de A B 

A la Tangente de BD 

Etant trouvé B D^ fe maaifcfte auffi C D« 

X. Comme le Sinus de CD 

Au Sinus de BD 

Atnji la Tangente de ABC 

A la Tangente de A C D 

KemurejUe. 

. En U première & féconde figure , 1 angle A C D eft 

le même que A C B : mais en la troifiéme ayant trotf- 

vé A C D , il faut prendte fon complément à iSo de* 

^tez , pour avoir Tanglc «quis ACB. 



y.*J?JLop. Clans copnusdcuxeôtcz, &rangleopp(>* 
fi à l'un des deux , trouver l'angle oppofé a l'autre i 
y^ AiByennanijju'onfçAçhe s'il ^fi digm 9h obtMSi- 

l': Çmm€ le SinHs du cote offoff à l'angle connu, 
\, Ah Sinus de t angle connu ; 
jiinjîle Sinus de Vautre côté connu, 
'Au Sinui de f'anglt requis* 

VL Prop. Etans connus Jjcç t|pi$<:ôtje9 » trouver 
lecjuel oti voudra àz% angles. 

^5oÔtez ejifcmbie les trois çôtçz , & de U îDoitic dé 
îciir fomme (buftray CE chaque côte comprenant Tan- 
glë requis > bdul: >voir leurs dtfer€nces< Apte^ celai 
^fuivc» ces deux anj^lo^jes. 

jf^Comme le S^s^us de quelqu'un ^s citez* com^re-^ 

17'^^^. ff^^s l*T0tgle reqffis y • * 

\ \ Ad.Sinus deVpihè des differeffées troUi^ùs : 

iÂhtJi le Smus dé /autre diffirknc<f, 

\ \ A ftn^qHatriétne^ Sinus. ' . 

.^vCofjfmé le Sinus de Vautré cêté^eomprgnant Van j^ 
gle requis, , 

Au Sinus fotaly' ; ' / 

* Ahjfile quatrifmé'SinUs tréuvé\. . .\ . ^ 

A un fepiénie Sinus* , . 

Ce Çcptiéme Sîpus étant muïtipUc par le Sinus to- 
tal, ktacine quarrée du produit fera le Sinus delà 
tticÂic de l'angle requis. ... > v . 

Ou plus facilement par Logatithmesl , ijoûtez le 
Logànthmc du Sinus total au fcptiémc Sinus Loga- 
ritlwnâque-.la moitié de la fommcf<ira le Logarithsic du 
Sinus de la moitié dei angle requis. 

Ou bien àjoûtezrles compicmens Arithmétiques de» 
io^arithmcs dés Sinus des cotez comprenant l'angle 
requis , aux Logarithmes èit% Sinus des différences 
tfouv'ëes : la moitié de ia {bmqae fera le Logarithme 



f 



CtiAP. V. Dts TriâHg. Sfhtriq. oUiq. H 



Ha Sinus de la moitié de l'an- 
gle requis» donc voicy un exezn« 
pie. 

Au Triangle A CD font 
connus les côcez B D 41 d; 8^ 
AÇ30 d: ô. & CD24d:4. 
On demande Tanglc A C D. ' 

41.8' 
30.0 
14.4 




AD 
AC 
CD 



La (bmme des cotez 

iLamoitié 

ta ditfer.deAC 

La ditfcr. de C D 

La foniDic 

La moitié eft de 

Le double eft 



ii.6 
14.x 

51.58 



Comf1, jirithf». 
o.30io50{i 

0.3895SJ5 

Logarithmes* 
5^-49i}o8| 
9. (^ o 9 8 8 o 3 

de ACÎ> 

VILProp. Etans connus les trois angles 9 tfomct 
lequel on voudra des côitez« ' 

En changeant les angles en leurs cfttc^ oppofeï 9 6t 
prenant tu lieu du plus grand angle 6c du c6té oppofé 
a cet angle > le compleinént à 180 degrez , l'opération 
fera tout de mSme comme en la précédente. 

V 1 1 J. P R o p. Etans connus deux angles , & un côté 
oppofé à l'un des deux trouver le ci^té oppofë i 
l'autre : Moyennant ejH'^tn ffocbe s' il e^ moindre oh 
flui grand fue le quadrant. 

Comme le Sinns de l'angle oppos/an cSt/connu g 

Ah Sinus du mime côté: 
Ainfi le Sinus de l'autre angU connu , 

Au Sinus du c6t/ requis* 



I X. P & o p« Etans connus deux cotez » & ràngfe 
(qu'ils coinptennenc» trouvetlé cioifiémc c&céf. 




%• Comine le ^jnHS total > : 

^u Sinus du complément dé A B C 

Ainfi U Tangente dé A B 

AU Tangente de BD 

^ Etant trouvé B D , l'on conhoic auffi C D. 

f. Comme le Sinus dû complément de É D 

Au Sinus du complément de C D 

: A^^ l^ Sinus du complément de . A B 

Au Sinus d» complément de AC 

%. P Ji'o p. Etans connus deux angles » & le coté pp. 
pofé à 1 un dies deux , tfouver le cotdcmie les angles 

; connus : Moyennant ^u'on ffache file cSt/^ requis , 
ou bfen le cet/ oppojé à Vautre angle connu , r/F 
moindre ou plus grand que le quà£ranti 




\. Comme te Sinut total » 
Au Sinus du complément do 

Ainfi la Tangente de 
A la Tangente de 



Ç J> 



ABC 
AB 
BD 

i. Comme 



CitAP.V, Des Triàng. Spbtriq. ^Uin. ^^ 

if^Comme la Tangente de A C B 

^la Tangente de , ^ ABC 

Ainji le Sinus de . BD 

Ah Sfnus de CD 

Si la perpendiculaire tombe dânl le Triangle 5 la 
fqnifflc de B D yC D : (î dehors > lOir différence ifk 
ie côté requis BC. '" 

XI. PnoP.Etansconnus deux cotci ,& l'angle ôp- 
pofé i l'un des deux , trouver le troifieme côté. 




1. Cmme ie Sinus total , 

' Au^ Sinus du complément de ABC 

Amp la Tangente de AB 

A la Tangente dfi BD 

1. Comme le Sinus d»tomfte$Hent dt A B 

Au Sinus du complément de A C 

Ainfiie Sinus du complément de J- R 

AtÊ Sinus du complément de CD 

Si la perpendiculaire tombe dans le Triangle, la 

fûrômc de B D , C D t fi dehors $ Itur différence cft 

le côte requis B C* 

XII. P Ro p. Etans Connut deux ahgks , & le côté 

d'entrc-deux , trouver Icqueh on voudra 

des autres cotez. 

Remarqué • 
En ce cas la perpendiculaire doit neceflaîremcfll 
tomber de Tangle connu adjacent au côté reculs. 



34 C H A p. V. Dei.TrUHgl. Sfheriq. eiiiq. 





^<^B 

I. Comme te Sinus total , 

Ah Sinus du complément de ^ A B 

Ainji là Tangente de ABC 

A U Tangente du complément de B A D 

Etant trouve B A D , fc xnartifeftc aufli CAD. 

i. ComtHè le Sinus du complément de CAD 

Ah Sinus du complément de B A D 

Aif^fi la Tangente de A B 

Ala T^angente de .• .AC 

Abrégé de ^u^ions Aftronomi^uây. ' 

t; TJ Tant connue la plus grâhdfc obliquité de ITkfi- 
JEptiquc, & ladiftancc 4i ScJcil »i-plus proche 
Ec^inoxe , tretavtt fa dcdin^ifon. 

tomme le Sinus tdtàt j 
, \^^ Sinus de la dijhndè m pt^s ftèche £dfU4W^xei 
Ainjî le Sinus de Id plus g^lMk èfhii^Ui^, 
Au Sinus delà déclinai fin reéjUife. 

îï. Etant cohnùc la plus grabd* okliquité de l'Edi- 
ptiquc , & la déclinai fon du Soleil,. iïouv« le lied 
. du Soleil dans TEcliptiquc.. 

Comme le Sinus de la plus grande obliquité de l'Ècli^ 
ftitjue , . . 
Au Sinus de la declinaifin du Soleil ; 
AinJi h Sinus total , 

Af^ Sinus de la diJlAncé dn Soleil au plus proche 
Bqninoxe^ ^ ' 




iprc- 
:confc- 
<juenc il faut opérer poui Us dcclinaifons cxaétes. 

III. Etant connue la plus grande obliquité de rEcii- 
prique. Se la diftance du Soleil au plus proche Equi* 
noxe> trouver fon Afcenfion droite. 

Comme le Sinus tôt 41» 

Ah Sinui du complément dé ta fins grande ^bliqnitty 
Jlmfi bk Tangente de la défiance dn Soleil auflnsfro- 
eheEqninoxe , 

A la Tangente ^de4' Jlfctnfion droite requife. 

I V. Etant connue la plus grande obliquité de TEcli^ 
:-ptique , & iàdtctinairon du Soleil » trouver 

i . fbti Afcenfion droite* v 
Comme le Sinus total i 
: AlaTangente deladecUnaifon du Soleil i 
. tMfrifi M Tangente dss complément de la f lus grande 
otliquité^ 
Au Sinus de Vjijcfnjion droite reqnife. ' 

y. Etant connue Isplus ^ande obliquité de PEcIipti- 
quç;, &JadiftancedttSolcAai^ pUis /proche Equi- 
noxe , trQuyer l'angle que rEçlipnque fait ^ avec ]fi 
Méridien; 
Commi^le Si^ûs total i \ 

Au Sinus dù-éhmflément de Ik difiance du Soleil 
au plus proche Eqsiinoxe^ 
Ainfi. la Tangestitdje la plus grande obliquité , 
A la Tavgemê du complément de fan^e requis. 
VL Etant connue la plus grande obliquité de l'Eclipti-^ 
que> Se la decliuairon du Soleil , trouver latigle 
que rÉcliptîque fait avec le Méridien. 
Comme lé Sinus du complenfent de la dficlinaifçn dsf 
. Soleil,, , ,; 

Au Sfnus dficompL de la plus grande oUiquipé} 
Ainjî le Sinus total 

Au Sinus de Vângle requis. 
■ C ij * 



3C Ahngédis J^ejlions AJlrcnomitjiêe^s. 

Vit* Etant connue la declinaifon du'Soleil y & Tél^ 
vation du Pôle i trouver l'ampUcude Orientale o\x 
Occidentale du Soleil. 

Comme le Sinus ducemplem. de V élévation in Pçte , 
Au Sinus de la declinaifon du Soleil j 

jîinfi le Sinus total , ^ 

Au Sinus de V Amplitude re^uife., 

yill. Etant connue la diftancé dtt Soleil ^au pluspro-" 
che Equinoxe , & fa plus, grande. ArapUtude , 
tR»uver les autres. Af&pUcttdes. \ ^ ' .. 

<lomme le Sinus totale '• ' " ^.r:- .V r 

Au Sinus de la f lus grande Amplitude d^'SdMls 

Ainfi le Sinus de Jà dipakce au-f lus proche Equinoxe 
Au Sinus de l'amplitude refuifié. ( .\ ^v:...'V3 

IX. Étant connue la dcclinaîfoû dû Sblçîl ;, Jfe Icle- 
* vation du Pote , trouvet la' diffctclnce Afcjciifîonèlle. 

Comme le Sifius total ^, ; r ' . ^ j.» 

. . A la , Tangente de la decîjnaifqn du Soletl i 
' : Ainji. là iTangenti^e VÏl^ydiidn du Pifé ; '' ' • '' 
Au Sinus de la ^i'grrèncc AJcenJionek^^^ 

X. Etant connue fa declinaifon 'du 5^oleiL,'&Vâcva- 

tion du Pôle , trouver rhcurc.du^ Icycr pm,*> 
• du' coucher, ilu^^oïcil* 

Comme le Sinus total 'y:-'. 

A là Tangente de Ik decUnaifondû S^lèU : 
Ainfi la; Tangente de Vélevation du Pote y ^ 
•Au Sinus du complément de VatcfeminoÛHrne. 
L*Arc femînoifttirne réduit en tiçmps , donnera l'heu- 
re du lever du Soleil , cjui ctant otc de ii, heures , il 
reftera l'heure du Coucher. ' 

XL Etant connue rEleyatipn du Pôle ,& l'heure du 
lever ou coucher du Soleil , trouver fa declinaifon , 
& partant à quel jour il fe lève & couche a rfaeu- 
xc donnée. 



Abrégé iè ^jie fiions Afironomiques. ^ jy 
Comme le Sinus total, 

Afè Sinus de U difiance du Soleil du Midj / 
A'tnfi la Tangente du compL de V élévation du Pôle , 

A la Tmgente de la Declinaifon requife. 

Maintcnaqt pour avoir le jour auquel le Soleil fç 
levé & fc couche à l'heure donnée , faites cette ana-^, 
logîc. 

Comme le Sinus de la f lus grande obliquité de rE^ 
cliptique y 
Au Sinus de la déclinai fin du Soleil ; 
Ainfi le Sinus total , • 

Au Sinus de^ la difiance du SoUH au plus pro^. 
che Equinoxe. 

XII. Etant connue Télcvation du Pofe , la déclinai (on 
du Soleil , ic Theure du jout » trouver la hauteur y 
du Soleil. 

Cette Méthode fuppofe la perpendiculaire tirce^d»' 
Pôle de l'Hotizon fur le cercle Horaire du Soleil. 
i. Comme le Sinus total , 

A la Tangente du complément de Vélevation 
du Pôle ; 
Ainfi le Sinus du complément de la difiance du So- 
leil du Midy , 
A la Tangente du premier arc trouvé. 

Depuis fix heures du matin jufques à fix heures 
du foir, ôtezie premier arc trouve deladiftançe du 
Soleil du Pôle , mais il le faut ajouter depuis les fix 
heures du (bit jufques à fix heures du matin , pour 
ayoir le fécond arc trouvé. 

I. Comme le Sinus du compl. du premier arc trouvé^ 
Au Sinus du complément du ficond arc trouvé y 
Ainfi U Sinus de l'élévation du Pelé , 

Au Sinus de la la^ hauteur requifi. 
Pour trouver la hautepr du Soleil à fix heures,, 
CxAvcz cette analogie. 

C iij 



5^ Àiregf de ^^efiions jffiron^miqueu 
Comme h Sinus total, 

j4u Sinus de la declina'tfon du Soleil : - 
Ainji le Sinus de V élévation du Vole , 

Au- Sinus de la hauteur reefuife. 
l^our avoir la hauteur da Soleil au temps des Eqoî- 
noxes , dites > 

Comme le Sinus total. , 

Au Sinus dû complément de V élévation du f oie i 
Ainjile Sinus du complément de la difiance du Soleil 
au Midj , 
Au Sinus de la hauteur, requife. 

XIII. Etant connu TAzicnuth & U dedinaifbn da 

Soleil ) avec Theuce du jour , trouver 
la hauteur du Soleil. 

Comme U Sinus de l'Az,imuth du Soleil du Méridien» 
An Sinus du complément de fa declinaifon ; 

Ainfi le Sinui de fa diftance au Midy , 

Au Sinus du complément de la hauteur reifSiifi. 

XIV. Etant connue* la déclinaison, la hauteur ».& 
TAzimuth du Soleil, trouver l'heure du jour. 

Comme le Sinus du complément de la declinaifan > 
Au Sinus du complément de la hauteur , 

Ainjtle Sinus deVAz.imuth du Méridien , 
Au Sinus de la difiance du Méridien. 

Cette queftion cft fort mile pour trouver l'heure 
plus facilement que par la fuivante, pourvu qu'on, 
^t une ligne Méridienne Horizontale bi«î tracée , ou 
un bon Aimant : parce qu*obfervant avec 1 ombre d'un 
iîlet Tangle de l'Azimuth en même temps que la hau- 
teur, vous aurez l'heure par une feule analogie. 

XV. Etant connue Télevation du Pôle , la declinaifon , 
& la hauteur, du SoleiU trouver rhcure du jour. 

Ajoutez enfemble ces trois chofes : Le complément 
de Tclevâtion du Pôle \ la ^î^%tkcc du Soleil du Polc y 
& le complément de la hauteur du Soleil : & de la 



moitié de leur (bmmc fouftraycz^ le' complément de 
Télevation du Polc^ ScU diftance du Soleil au Polc^ 
afin d'avoir leurs différences. Après cela faites ces 
deux analogies : 

1. Comme le Sinns du comflement dé l'élévation dn 

Pôle, 
Âh Sinus de Vune des différences trouvées ; 
Ainfi le Sinus de Vautre différence , 
ji un quatrième Sinus* 

2. Comme le Sinus de la difiance du Soleil au Foie y 

Au Sinus total y 
jiinfi le quatrième Sinus trouvé ^ 
A un feftiéme Sinus. 

Ajoutez le Logarithnoe du Sinus total , au feptiénie 
Sinus Logarithniique : la moitié de la fomme fera le 
Logarithme du Siaus d'an arc , lequel étant doublé û 
teduit en heures , donnera la ^ift^ce du Midy.. 

Ou bien ajoutez enfemble les complemens Arithi> 
metiques des Logarithmes du Sinus du complément 
de l'élévation, & du Sinus de la diftance du Soleil au 
Pôle , &^ les Logarithmes des Sinus des différences 
trouvées : la moitié de la fommc fera le Logarithme 
du Sinus d'un arc , dont le double étant réduit en heu^ 
res donnera la diftance du Midy. 

Cette queftiori tombe des plus en pratique , & fe 
refout par la(». Prop. du Chap. V. des Obhquanglcs» 
Car au Triangle ABC, les trois cotez font donnez. 
C, eft lePole. 
B,rAftrc. 
A C , complément de 

la Latitude C K. 
A B , complément de 

la hauteur BH. 
BÇ, diftance de l'A- 
ftre au Pôle » qu'on 
i^ait en otant fa decUnâifon de 90. degrez , quand 

C ui) 




4<> Alregi àe ^ueJUons Àflrônomiqies. 
€llc cft Septentrionale , & l'ajoutant i ^o. Aigtt%^ 
lors qu elle cft Méridionale , &: qu^ la Latitude cft Se- 
ptentrionale : car fi elle étoit Méridionale, il faudroit 
opérer tout au contraire. 

Le requis, cft l'angle A C B > ou la diftancc de l'A- 
ftrc B au Méridien 1 A mefuréc par l'arc de l'Equa- 
tQUr IL) qu'il faut réduire en heares , en le divifanr 

par 15- 

Or cette Qaeftion fc refout plus facilement par Jjc 

4cf nier précepte » ç'eft à dire par les complemens 
Arithmétiques , que par les autres opérations. 
£tant cofinné l Elévation du^ Pôle , la hauteur ^ çj- la 
Declinaifon d'une Etoile , trouver l'heure 
de la. nuit. 
' . Il faut faire comme pour le Soleil , & on aura l'an- 
gle A C B , ou la diftancc de l'Etoile au Méridien , 
îaqucllc il faut ôter de fon Afccnfion droite , fi Tob- 
fcrvation cft faite dans la quarte d'Orient , ou l'ajoù-* 
ter, n elle eft dans la quarte d*Occident : & on aura 
TAfcenfion droite du milieu du Ciel , de laquelle 
enfin fi on ôte TAfcenfion droite du Soleil , il reftera 
la diftancc dq Soleil au Midy paflc , laquelle étant 
rcdqite eh temps donnera l'heure requifc. Mais , fi 
l'Afcenfion droite du Soleil fe trouvé plus grande que 
celle du milieu du Ciel , il faut ajouter à cellc-cy 
jtfq. dcgrez, pour en pouvoir fouftraire celle-là, afin 
d'avoir la diftancc requife du Soleil du Midy pafle , qui 
eft l'heure que l'on cherche , étant réduite en temps d 
15. dcgrez pour heure. 

Étant conf^ le lieu du Soleil , ^ V Elévation du "Bole , 

trouver l'heure du commencement & de la fin 

^ des Créfufiules. 

Dautant qu'on détermine ordinairement la durca 

des Crepufcules par le temps qac le Soleil cft abaillc 

fous l'Horiaon , j^ifqucs à 18. dcgrez , étant certain 

qu'il employé le même temps à defcendrc de 18* de, 

grez de hauteur jufquosçnl'HQriaBonque de THori^ 



zon jafques a 18. degtez ou deâbusr, qui tftléCre* 
pufcule du foir 9 & é^ tn&me â monter le tnatiti. 

De façon qu'ayant l'heure de la hauteur , &fçachànt 
celle du lever ou du coucher par la Queftion lo. leur 
dijffcrcnce fera la longueur du Crepufcule , laquelle 
étant ôtée de Th^ure du lever du Soleil , vous autes 
le commencement duîour,& étant ajoutée à l'heure 
du coucher du Soleil » vous aurez U fin du jour. 

XVI. Etant connue l'Elévation du Pôle , laDedinai- 
fon & la hauteur du Soleil, trouver fon Azimuth. 

Ajoutez enfemble ces trois chofes : le complément 
de l'Elévation du Pôle , la diftance du Soleil au Po« 
le » & le complément de la hauteur du Soleil , & do 
la moitié de leur fbmme (buftrayez Le.complement de 
l'Elévation du Pôle y & le complen^ent de la hauteur 
du Soleil , afin d avoir leurs difFcrenceSt Après cela 
faites ces trois analogies. 

I* Comme le Sinus du comblement de l* Elévation 
du foie , 

Au Sinus de l'une des différences trouvées | 
Ainji le Sinus de l* autre différence , 

A un quatrième Sinus' 

X' Comme le Sinus du complément de la hauteur du 
Soleil , 

Au Sinus total , 
Ainfi le quatrième Sinus trouvé , 

A unfeftteme SinUs. 

Ajoutez le Logarithme du Sinus, tolalaufeptiéme 
Sinus Logarithmique : la moitié de la fomme fera le 
Logiarirhme du Sinus de la moitié de l'Azimuth re- 
quis du Septentrion. 

Ou bien ajoutez enfemble les complemcns Arith- 
métiques des Logarithmes du Sinus du complément 
de l'Elévation du Pôle , & du Sinus du complément 
4w la hauteur du Soleil > icUs Logarithmes des Sinus 



4t JÈiriffie ^fffftimi '^AJhûnmi^Ufr. 
éai 'Stkfcnots trouvées : la nsoicié 4e 1^ Commit Çct^ 
le Logarithme du Sinus de la moitié (ierÂziinmhie-« 
quis du Septentcioa* 

Cette qoeftion fe cefbut comme la précédente pac 
la 6. Prop. des Obliquangles > les tcois cotez du Triafi-» 
gle AB C étans donnez eti la figure de cy-devant : 
car ayant trouvé Tangle C A B » fon complément BAI , 
ou H AM fera l'Azimuth requis du Mtdy i l'Aftre. 

. Elleeft fort utile pour la (7)^awoif/^jy^ & la varia^^ 
iioH, ic VAjmAnt , car en pbrervant la hauteur du 
Soleil on peut marquer fur un plan Horizontal l'om* 
bre dun filet perpendiôtlaireî pms> VandeAzimu* 
thaï étant trouvé par le calcul > & tracé iur le piM , 
on â bu la ligne Meridèene , ou la lipté OriintaU y fé- 
lon qu'on a pris le compkment de l'angle CA B fut 
iSo ou 90 degrez » par Tune ou l'autre defquelles on 
trouve la variation de l'Aimant. 

Pour faire les Tables d'Azimuth» (èrvans àla Gno^ 
monique &c aux Qgadrans de l'aiguille aimamée > i! 
fuific d'y mettre les commencemcns des Signes. D» 
Henrion en a fait pour plufîeur$ Elévations dans (on 
Traité des Triangles Spncriques. 

Pour trouver 1 Azimuth du Soleil à 6. heures , fut- 
vez cette analogie. 

Comme le Sinns total, 

Af* Sinus du complément de VlElevatlon du Pôle, 
A infila Tangente de la Déclin ai/on du Soleil, 

A la Tangente de l'Ax,imuth du Soleil vers le 

^ . Septentrion. 

Pour trouver l'Azimuth du Soleil au tctops des 
Equinoxes , faites cette analogie. 

Comme le Sinus total , 

A la Tangente de l* Êleifatio» du Soleil i 
A n fi laTangente de V Elévation du Pôle , 

Au Sinus du Cûmflement de VAx^imuth reculs 
du Méridien^ 




'jttregi Je J^ftiàns jtfim'nûmiqnetp . 'jff 

X ^ H. Deux hauteurs de Soleil od4ie quelque Aftre »' 
dont la Dedinaifon foit connue, étansobiîbtvéer 
en un joucouen uneiittit> aveiclairdi&feocrAjsW 
mutalestrouver TEIeirationdtt Pole»& leur Azimuth^ 

AB.CD eftlçMeridien, 

C Zenith. D Polc. 

BEprEquateut. 

AIL l'Horizon. 

G,& H , le Soleil) ou 
TEtoile. 

G£,&HKl€ur Dedi^ 
iKiifbn. 

G I , & H F leur hasiteur. 

IF dtfference Azimatale. 
On demande TElcTa- 

tion du Polc D L , & Tare de l'Horizon L F « ou A I ^^ 

ou AP. 

Pmfqu au TriangleC CH , les deux cotez G C , & 

H C , complcmens de G I , & H F , & l'angle G C H ^ 

qui eft IVrc IF, font connus t TarcGH, & Tangle 

GHC feront auiS connus. 
Mais, au Triangle GDH,lesc&tezGD,&HD, 

eottplemens de la I>eciinaifen GE , HK, & GH 

ctans connus , l'angle G H D fera auffi connu > duquel 

fi on 6tc G H C , reft^ra l'angle C HD : &: partant 

dans le Triangle C H D , les deux cotez C H , & 

D H , & Taille qu'ils comprennent , étans connus » 
le côté C D fera auffi connu » dont le complément 
D L eft VElevathn du Pôle. Comme auffi l'angle 
D C H , qui eft l'arc derHorizon F L , dont le com- 
plément A F eft Tangle de la ligne Meridiene & de 
TAzimuth de rAftreobfcrvccnH. Mais fionnepre- 
noit que F L , pour complément de 90 degrez , ou 
auroit l'Azimuth de la ligne Orientale Septentrional, 
fi ledit arc F L étoit moindre que 50 degrez , ou Mé- 
ridional 9 s'il écoic plus grand. 



4^ 'Mnglde ^^hnî AftroHèmiqueî. ^ 
"^ Cette Queftion fe peut aiftmeiit réfoudre avec le 
compas (iir un Globe» oillles Âzimmhs ti\t$ Almu- 
cancantts (bnc tracez , en mettant la pointe du compas » 
ouvert des degr^z 'H D » fur les points H , G , & en 
£dfanc dèusc inter feâions de cercles au point D , qui 
fera le Pôle , duquel on verra la hauteur 17 L , & Tare 

L'utilîté eft gràhd^our Ixvéiriatian de t* Aimant , 
parce qu'en ob^ctvant l'angle de quelqu'un de$ h^i^ 
mâtbs avec rkigiiiUlé , bn^rçait cejby! qu'elle fait avec 
I^ Méridien , quand^Ue eft par après trouvée , ce 
cji'oîî litf pcut^fakc que par les Afûplitudcs , ou par la 
Ii§ne l^endiene , que Ton n'a point fur Mer. 

Elle fertauffi pour \k C7if^9iM»/^^ aux plans Hori- 
zontaux f mais infiniment plus en ^tous plans qfiicU 
qu'ils foîentren ofcfervant deux p 
points d'ombre B , C , de U 
pointe d'un ftyle D , de l'inciden- 
ce de laquelle A, drant deuxli* 
gnçs A B y h Ç '9 on aura Tanglc 
ou différence Azimûrhale BAC » 
la longueur de chaque ombre ^i ^^ 

A B i AC , & la h^tcut du ftyle , ^ 

AD, donner^ la hauteur du Soleil fur le plan lors da 
chaque obfervation. 

Partant on eft dans les termes dçla queftion, pat 
lefqueh on trouvera l'art- , 
gle de la ligne Meridtene 
du plan , qu'on appelle //- 
gnc du Style ,. avec quel- 
qu'un des Azimuths AB, 
ou A C , laquelle ligne 
Mcridicnc ayant tr^cç fui- 
yant cet angle, 8c. fur cette ligne FAE ayant élève 
le ftyle pcrpcndiculaitc A D , on fera l'angle A D E 
complément de la hauteur du I?ole furie plan , laqucU 
le ou trouvera comme il a ctc ôafcignc cy devant. Le 





point £ fera le Véritable Pôle ott centre du C^a^an 
de ce plan ^ duquel' abâiflànt ou traçât la: vericliblc 
ligne Metidienriey ^ tinCnt le rayon Equinoxi^ Dï'» 
on fera dans lei$' tel?À>es dé parachever ficilcmetit fe 
Qàadratic, &de%Vok, ïî'onvcut, PélcTatiôtt db 
Pote an lieu 9 lâDediMtfon du plan, &6 llktify^ 
fe faut fervir du jiTgeméif t en la détermîiiatioti de HVit* 
^linailbn, Inclinaifonj &;.autFë9^<:ireoilftancés-s'il7en 
^ ,'ruivanr. les Règles de la Qnomonique qu'il fefok 
jtôp long de dedviKÇ içy par, le menji* - 

}^VIJL Etant coi^niië rélevationdu Pôle , Jk I^di^an» 
ti^^' Soïçiï ah Mcn4iciii ^ qui cft rhcure , trbuycf 
ï^tc de l*Hori2;oîi éofnpriî entre .ce ^ïeri^icn & ]c 

♦ ccfêie' rîof àirc' ' ■'' ■ \ : . . ' \ -^ ' ', ^ • ; ■ '■ :'; :'■ :" '/ 

Çpmmfi le SinH$ t^tal »' -• ' .-r...*: jr:? ..::. • .j ûi 

j< /4 Tangente de l'arc requis. of.n 

, Par Ji- oarfçra^facilemçnr^.^y,«q.jçflw(ïe .un Qgjt 
dcanc Horizontal , parce: quç iï^i.fiiicçf i^ç llHif^ifûn 
jfont ïcRÛI)lç9\cntég^U3ç aux ftû^efei^S.Ji^UlISf éti- 
res avec la Meiidiene. -r r ri;\'i'f> fîf •\^..I-7 
XIX/Ekant connue ktx>o'gttude^'^4atatitiidè^dVtic 
:, . .•---Etdllc;fixe,:ttouvetf4raI&eU«aiîbn^^ ^ 
AEB cft l'Equateur. 
P,fohPolc: 
S 3 Vf rfls^ >»> le 

Zodiaque. 
Z , fon Pôle. 
APZ » Colure des 

Solftices. 
C , TEtoille donnée , 
de laquelle G T. A 
Longitude » G C fa 
^âtude Ibnc 'doiÀ- 
nues. 




^ AhegéJè ^têefiiàns Afii^ûÀùmiil$Uié 

<ptlt Patigle D B N Aziniuchal par obfirrvaEÎoni. 

Donc au TriangU AtBC deux cotez A C , C B « ft 
i*angle CBAco^^lctneac de TangleDBN % étant 
xlonncE» on trouvera Tanglefi^C A ^:qui eft.rarc lA 
ou H M } lequeL étant divifé. pat 15 degtez > lé quo^ 
tient fera le nombre des heures requifès. 

XXI IL Etàfkt cbnhuë là Hiutéur ficlaDedinaifoiX 

du Soleil , ay^c l'angle Azltnuthal , trouver 

. l'heure. &rEleYation duPole.^ 

L*arc B A complément de la hauteur du Soleil A I# 
eft dgpné, A C eft auifi donne > l'angle Azimuthaleft 
au$ donné > Donc^^ ^ 

' Câmme le Si^s de V Arc A C^ 

Efi émSituu^deVangle ABC % 
\Ainfi le Sinuê-de AB3 

£fi aià Sinus de l'angle ACB, ^Hi efi V^rc 
\.^ tAon H.M y four l'heure requife. 

£( pour rElevation du Pôle» voyez l'Analogie pour 
trônver le<ôté BC » complément de la hauteor du 
PoleCF, 



TABLÉS 



TABLES 

DE sinus: 

TANGENTES, 

ET 

SECANTES, 

Pour un Rayon de looooooo parties,' 
ET D E S 

LOGARITHMES 

DES S IN U S 

ET DES TANGENTES, 

Pour un Rayon de loooooooooo parties. 



c 



lo 
II 
li 

15 
14 

16 
li 

^9 

10 
zi 

IZ 

*4 

iJ 
z6 

z8 
i^ 



Degrcz o 



Sinus Tangent. Sécantes. Log.Sin. Log.Tting 



19.09 
/8.18 

87.Z7 



116.5^ 
i4y-44 
174/3 



z^.05^ 
;8.i8 

«7-t7 



Il^.jéllOOOOO. 

141.44 
174X3 



Z03.6Z 
Z3Z.71 
Z61.80 



Z03 

Z3Z.71 

261.80 



190.%9 
Il9'9% 
34^-of 



z^o.8^ 

3I5>.^« 

34^07 



378.1/ 
407.Z4 
43^-33 



46/.4Z 

4i>4/i 
jZ3.^o 



//z.<8 

/81.77 
^io:$6 



^i99S 
469JO^ 

é^8.i3 



7Z7.ZI 
7/6.50 
7^Si9 



814.48 
843/7 



378.16 



43^-33 



100000.00 



100000.00 

lOOOOO.OZ 

1 00^00.^4 



07 
100000.11 
100000.16 



6z looooo.: 



11 

1 00000. Z7 
100000^3 



100000.4Z 

lOOOOO./I 

100000.61 



I00000.7Z 



407.11 X 00000. 8 3 



1 00000 .^j 



46J.41 iooopi.08 

4^4.ji 10060 1. IX 
/Z3.^ 100001.37 



Sf^^9 
/81.78 
^10.17 



6}996 
69%, 



téy.^s tcaoo 



14 XOGOOLi 



7i7-*3 

7/<i^-3 

78/-4I 



8i4.;o 

843. 

871 



100001./3 

r 00001.70 
îooooii>7 



looooz.oj 
44 



loeooa.^/ 

îlOQOOZ-86 

100003.08 



100003.31 
80 



60 100003. 



6^100003. 



6.4637Z61 
6.7647/61 
6.9408473 



7.J088Z39 
7.36681/7 
7.4i7i?68i 



7-4^372'/X 
7./0/1181 
7./4Z906/ 



7.06/7860 
7.16Z6560 
7.Z418771 



6.4637161 
6.7647/61 
^.94oS47/ 



7.06/7863 
7.1616564 
7.1418778 



7.3088148 
7.3668169 
7A179696 



7.4^37173 
7./0/1103 
7-/4 1909 r 



7./77^4î8f[7./77^7i/ 
7.6098/30 7.6098/66 
7.6398160 7.6398101 



7.667844/ 

7.^5>4I733 
7.71899^^ 



7.741477/ 
7-7^47/37 
7-78/9417 



7.80614/8 
7.81/4/07 
7-^43 5^338 



7.86x6^15 
7.87869/3 
7.89/08/4 



7.9108793 
7.9161 190 
7.9408419 



7.6678491 
7.694178^ 

7.7x9001^ 



7.74*4841 
7.7647610 
7.78/9/08 



7.8061/47 
7.81/4604 
7-84)^444 



7.8^1673.8 
7.8787077 
7.89/0988 



7.9x08513* 
7.9161544 
7.9408/84 



s 



89 Dcgrct, 



Sinus Tancent 



^o ipoooo.oo 



5999999-99 



Infîn 



343774««7- 



;8W5>9.^8 171887519 



5^\999999^\^}9^}é^o 
S S 99999*99^^75^^^7 
5^99999^5 57^957^^ 



S y 99999 7 9 
S^ 99999,7} 
f ^[99999*66 



49IloéOo 
419717/7 
§819709^ 



48 



99999' S^ 
9999949 
99999-39 



^799999^9 
9999917 



99999.o5\l^9^9iéG 



41 



409999%.^! 



99999-92. 
99999^79 
99999-63 



39 



Sécantes. 



Infinie. 



J4|774<8» 
171887} 48» 

i»459'î74 



85945^85» 
08714^^0 
nX9S9o9 



J4377^7i 
M*J2'I57 
18647773 



16444080 



+9110701 

+1971875 
38197150 



54377;i«- 
3iijfii97. 
18647548.; 



1011187J 
J909%4t9 



99999.47 



99999.13 



99991^95 
99997-7^ 
99997'S^ 



99997-3^ 
99997 -'i A 
3399996-91 



16444165- 
i4j;/40i- 
119x838/. 



11481761. ii49S99S 



J$093ti0. 
17188/40. 

16370019 



I/6z/^8. 

i494^;oi 
14313711 



99996.^% 
99996.é^ 
yo9999é.l9 



137/074; 
132118/1. 

11731134 



lOlllIXl 

9098680 



1*09345^ 
1^188851 
1637031/ 



i;6l6il8^^ 

I494<î837 

14314061 



11177396. 
118/4018 
114/886/ 



1 37/1108. 
131x111^ 
11731/16 



1I177803. 
118/4440^. 
iî4/5|Qt 



to. oooûooo 



9.9999999 

9-9999999 
9-999999^ 



Lo%, S in. 



Log Tatég. 



InHnk. 



^35369.739 
13.13/1438 
i3.of9i/i/ 



9.9999997 11.9341137 
9-9999995 11.8373036 
9.^999993 it.7/81111 



9.9999991 
9-9999999 
9.9999995 



11.6^117/1 
11.6331831 
11./810304 



9-9999991 
99999979 
9^9999974 



9'99999^9 
99999964 
9-P9999i9 



11/361717 

H.4948757 

1 1.4/70909 



11.411318/ 

j 1.3901434 

11.360179^ 



9-99999 f 3 
9-9999941 
9-9999940 



Ii.3}ii/ô8 
11.30/8114 
11.1809574 



999999i4 li.i/7/i/5 
9-99999±7^^^^i 5^390 
\9-99999r9 I1.1Ï4Q451 



99999i^ 
9-9999903 
9-9999994 



iyj84/3 
t745i96 
156955^ 



9-999999 s ïx^l 39 }%6% 
9-9999976 Ji.yiiz5i3 
9-9999966 11.1045911 



999999 f 6 
9-9999945 
\9-9999935 



II.085206X 
11.07386/^ 
11.0/5x614 

Aij ' 



5 

c 




Dcgrci 









Sinus 


Tangent. 


Sccantcs. 




Log. Sin. 


Logi Tang. 


jc 


%ix,6s 


871.65 


100003.80 


7.5408415 


7.5408/84 


51 
31 

33 

3/ 
3^ 


^Pi-74 
5»30.83 


501.78 
530.87 
9S9'9^ 


100004.06 
100004.33 
100004.61 


7.5/;o8i5 
7.5688658 
7.5811334 


7.9550996 
7.5688886 
7.5811/34 


1018.05 
1047.18 


585.0; 
1018.14 
I047-2-4 


100004.85 
1 0000;. 18 
100Ô0/.48 


7-99^9^0 

8.0077867 

8.0100107 


7.55J1151 

8.0078051 
8.010044/ 


37 
3S 


iioj.H 
1134.44 


1076.33 
110J.41 
1134./1 


10000/.75 
100006.11 
100006.44 


8.031515/ 
8.043 J005 
8.OJ47814 


8.0315444 
8.043/174 
8.0/48054 


40 
4.1 
42^ 


ii^3.J3 
119^.61 

1111.70 


1163.61 
1151.70 
iitî.75 


100006.77 
100007.11 
100007.46 


8.06/7763 

8.0764557 
8.0865646 


8.06/80/7 
8.076/306 
8.0865570 


43 
44 
4/ 


11JO.75 
1175.87 
1308.56 


ii;o.88 
IZ79'9^ 
1305.07 


100007.81 
100008.15 
ioooo8.j'7 


«.0571831 
8.107^1665 
8.1 165161 


8.0571171 
8.107101/ 
8. 11656.34 


46 
47 
48 


1338.0/ 

1367.13 
1356.11 


1338.17 
1367.16 
I35^-3J 


100008.56 
100005.3 J 
IO0OO5-7J 


8.1 164710 
8.13/8104 
8.1445 J3i 


S.1165099 
8.13/8/10 
8.14455/^ 


4J> 
J4 


141J.30 
I4J4.35> 
1483.48 


I41/.4/ 
I4J4.J4 
I483.<?4 


100010.16 
100010.J8 

lOOOII.OI 


8.1/3507/ 
8.1616808 
8.1711804 


8.I/35/I6 
8.1617167 
8.1713181 


1/11./6 

ij4i.^J 

,. i;70.73 


IJM.73 
IJ41.83 
1/70.53 


3^011.4/ 
1000H.85 
100011.34 


8.1757115 
8.1875848 
8.1561010 


8.1757616 
8.1880364 
8.1561//6 


si 


1S99'^^ 
1618.50 
I6J7.55 


1600.01 
1615.11 
l6j8.n 


100011.80 
100013.17 
10001 3. 7 j 


8.1040703 
8.1118545 
8.115/811 


8.10411/^ 
8.1115/16 
8.1156408 


s^ 

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10.5005554 
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TABLE 

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LOGARITHMES 

Pour les Nombres Naturels depuis 
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1.658x00/ 
1.6585700 



500 



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N. 


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1.699^^77 


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1.7/5/851 


yoz 


1.7007057 




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1.7185/38 




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1-7/43483 


S03 


1.70X/680 




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1.7014JO/ 




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1.70 j 151 4 




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1.7507815 




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1.7/^6561 


S06 


1.7041/0/ 


1.731/888 


/71 


1.7/7 3 i>^o 


SOI 


1.70/0080 




/40 


*-75i5^j8 




/73 


1.7/81/44 


SO% 


1.70/8^37 




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W55i^75 




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17/85115 


S09 


1.70^7178 




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î"75î^^^3 




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510 


1.707/701 




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1.708410^ 


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1.71 ï 8071 




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1.71x6497 


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1.7^45150 


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1.7405^17 




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1.7145158 




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1.74x1/1^ 




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1.71/1674 




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1.743.71/1 




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17478574 


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1.7484381 


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1-7x7^70/ 




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17453773 


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1.718/017 




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1.74/0748 




/85 


17701 1/3 


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1.71515IJ 




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1.74/8//1 




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1.7708/10 


Jî-J 


1.7101/55 




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1.74^^341 




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1771/87/ 


SX6 


1.71058/7 


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1^^474118 


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1.7713117 


J17 


1.711810^ 




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1.7481880 




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17730/47 


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1.711^335 




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1.7485^15 




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17737844 


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i.7iJ4//7 




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2-74^73^3 




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1.7/0/084 




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177/1445 


jj 11.71/054/ 


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1.7/117*1 


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177/5>74J 


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1.7/10484 




/>»8 


1.7747011 


/35 i.7i<^7i7i 




/^6 


1.7/18 U4 




S99 


17774148 


/J4 1.717/41 J 


S67 


1.7/3/831 




600 


1.7781/11 


-6qo' 



Coo 



N. IfPgarkh 

^o«2.7«o5i7| 
6pf 1.7817^/4 



^o4|i.7ti47xi^ 
6072.7851887 
608.2.781^05^ 

6o^|2.7«4^X7l 
6102.78/5298 



61XI2.7860412 
61212.7867/14 

615:2.787460/ 
614^2.7881684 
61/12.78887/1 



616 2.789/807 
6i7!2.790r8f2 
6i8|2.790988/ 
6i9j2.79i^^6 
6202.7915917 



6ii 
622 
625 

624 
61/ 



X'79}09i6 
^'791790^ 
2.7944««o 
2.79/1 M 
2.79/880CI 



62/ 
627 
628 
629 
650 



^51 
652 



1-7^^/745 
i-7^7i^7X 
^•7979S96 
2.7986/06 

2.7^^540/ 



2.8000194 
2.80071 71 
2.8014057 
2.8020895 



AT. Ligarkh 



«H 
65/ 
656 
^$7 
<5« 



^40 
641 
^41 
^45 



644 i 



^4/ 
646 

^47 
648 



^4^ 

^S3 



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6/72 
6j8 



660 
661 
662 
665 



664 

66s 
666 

667 



2.8020895 
2.8027757 
^•«054/71 
ii.«04I5^4 
2.8048207 



2.80//009 
2.8061800 
2.8068/80 
2.807/5/0 
2.80821 10 



80888/9 

2.809//97 
2.810252/ 
2*8109045 
2.811/7/0 



2.8122447 
1.8129154 
2.815/810 
2.814147^ 
1.8149151 



i-8ifJ777 
1.81 6241 5 

1.8169058 

817/6/4 

2.81822/9 



2.81888/4 

i'8i^/45^ 

2.820201/ 
2.8208/80 
1.821/15/ 



1.8121681 
1.8228116 

t.8254742 
1.82412/8 



JV. iLigsràth 



667 

668 
6^9 

670 

671 
«75 

*74 
«7J 
«76 

«77 
678 

«75 
680 
681 

681 
685 
684 
68/ 
686 

687 
688 
689 
690 
69 i 

691 
^9$ 
69^ 
695 

690 

697 
69^ 
69: 

700 



1.81412/8 

2.82477«X 
2.82/426X 
2.8260748 
2.826722/ 

2.8275695 
2.82801/1 

2.8286/99 
2.8295058 
2.8199467 

2.850/887 
2.8512297 
2.85x8698 

2.852/089 
1.8 5 j 1471 

' ' ' " " p 

«'•8|I7«44 
2.8544207 
2.85/0/61 
t. 8 5/6906 
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i«5«^/«7 
1.857/884 
1.8581192 
1.8588491 

1.8594780 

1.8401061 
i- 84075 51 
^•8415/5»/ 
1.8419848 
1.8416091 

1.8451528 

^•8458//4 

^•844477^! 
i.84f098Q 



700 



700 



jv: 

701 
701 
703 
704 
70J 



Làfftrith 

1.8457180 
1.846 j 371 

1.847/7^7 
1.84818^1 



706 
707 
708 
70^ 
710 



711 
711 
715 
714 
71/ 



716 

717 
718 
719 

710 



7X1 
7X1 
7^5 
7M 
7iJ 



7x6 x 

7^7 
7x8 
71^ 
7JO 



751 
73^ 
755 
754 



X.8488047 

x.84^41^4 
X.8/00333 
X. 8/06461 
1.8/IX/83 



x.8/i86^6 
1.8/X4800 

x.8/3o8^jr 
x.8x56^8x 

1.8/430^0 



x.8/4^130 
x.8///i^x 
1.8/61144 
1.8/6718^ 
x.8/7551/ 



x.8/7^3;5 
X.8X8/371 

i.8/5>i383 
x.8x^7586 
X.8603586 



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X.86I/344 
1.86X1314 
X.86X7X7/ 
x.8635ii^ 



X.8635174 
X.864XIII 
X.86JIO40 
x.86/6^6i 



754 
75/ 
756 
757 
758 



Lpgaritb 

z.S6s^9Sl 
X.866X873 
X.8668778 

X.867467J 
X.8680J64 



75^ 

740 
741 
74i 
745 



744 
745 
746 
747 
74? 



74^ 
7S0 
7 SI 
7S% 
751 



7/4 
7SS 
7/6 

7J7 
7/8 



759 
760 
761 
76X 
7<^5 



7^4 
7^5 
766 

767 



1.8686444 
1.86^x317 
X.865818X 
1.870403^ 
1.870^888 



1.871/71P 
1.8711/63 
1.8717388 

1.873310^ 
x.873^016 



1.8744818 
1.87/0613 
1.87/63^^ 
1.8761178 
x.8767^/0 



1.87757^5 
1.877^46^ 
1.878/118 
x.87^0^/9 
1.87^66^1 



1.8801418 
1.8808136 
1.8813847 
x.88i^//o 
X.88X/X4/ 



x.8830^34 
X.8836614 
1.8841188 
x.8847^/4 



AT. { JL0^4rr>i& 



767 

768 

765 
770 

771 

771 
775 
774 
77/ 
776 

777 
778 
77^ 
780 

781 

78X 
783 
784 
78/ 
786 

787 
788 
78^ 
7^0 
75»i 

7^1 
75>5 
7^4 
^95 
796 

797 
75>8 

799 
800 



1.88475/4 
1.88/3611 
i.88/«»i63 
1.8864^07 
1.8870/44 

1.8876173 
i.888i7^j 
1.8887410 ' 
1.88^3017 
1.8898617 

1.8^04110 
x.890^796 

1.85^1/37/ 
X.8PX0946 
x.8yx6/io 

x.8p3xo^8 
X.8937618 
x.8943l^x 
x.8^48697 
x.8^/4xx/ 

1-85/9747 
x.8^6/x6x 
x.8^70770 
x.8^76x7i 
X.898I76/ 

x.8^87x/i 
1.89^x73 X 
1.8998x0/ 
X.9003671 
x.900^X3X 

1.9014/83 

1.9010019 
1-901/468 
1.9030^00 

800 



8oo 



Soi 
8oz 
803 
804 
80J 



1.^041744 
1.90471// 

l.90jl/dO 



^o6 
807 
808 
809 
810 



1.90^33/0 
1.906873/ 
1.90741 14 
1.907548/ 
1.^0848/0 



811 
811 
813 
814 
81/ 



1.9090109 
1 905//60 
1.510090/ 
1.9106144 
1.^111/76 



816 
817 
818 
815 
810 



1.51 16501 
i.^iiiiii 

1.5117/33 
1.9131839 
1.91 381 38 



811 
811 
81J 
814 
81/ 



i.5143432' 
1.9148718 

2.51/3558 
1.51/5172- 
1.9164/35 



816 

817 
818 

830 



1.9169800 

1-5I7XOTJ 
1.9180303 

1-51 8//4/ 
1.9190781 



831 
831 
833 
834 



1.9196010 
L.9101133 
1.91064/0 
1.9111660 



N. ■Logarith 



834 
83T 
836 

837 
838 



1.911 1660 
1.911686/ 
1.9111063 

1.9131440 



835 
840 
841 
841 
843 



844 
84/ 
846 

847 
848 



1. 51/7610 

1.5141753 
1-5147560 
1.51/3111 
1.51/8176 



1.5163414 
1.5168/67 

1.5173704 
1.9178834 
1.51839/8 



845 
8/0 
8/1 
8/1 
8/3 



1.5185077 
1,9154189 
1.9195196 
1.5304356 
1.5305450! 



8/4 
8// 
8/6 

8/7 
8/8 



i-53 14/75 
1.9319661 
15314738 
1.9319808 

15334873 



8/5 

860 
861 
861 
863 



1-5335531 
1.5344584 
i-53;oo3i 
i-53no73 
1.5360108 



864 
86/ 
866 

867 



1.93^/137 
1.9370161 

i-537fi75 
1.9380151 



867 

868 
869 

870 
871 

871 
873 

874 
87/ 
876 

877 
878 

875 
880 
881 

881 
883 
884 
88/ 
886 



Legaritb 

1.9380191 

1-538/157 
1.5350158 
1-535/151 
1.54001 81 

1.540/16/ 

1.9410141 

1.541/114 
1.9410080 

1.941/041 
1-5415556 

^'9^H9^S 

1.5444817 
1 -54457/5 

1.94/468^ 
1-54/9^07 

^9^69^^$ 
i-5474337 



887 
8^8 
885 
850 
851 

851 
853 
854 
85/ 
856 



1-547513^ 
1.5484*30 
1.5485018 
1.5453500 
1.5458777 

1.5/03648 
2..5/08/14 

* 5/1 3 37; 
i:.5/i8l30 
1.5/13080 



857 

858 
855 

500 



N 



1.5/17514 
1.5/317^3 

i-5/37/^7 
1.5/4141/ 

90Ô 



5>oo 

JV. Lûgaùth 



901 
901 
505 

90s 



906 

907 

909 
910 



911 
91t. 

91S 



i-^J47i48 

1.^/^1684 
1.9/^^48^ 



x.^j7ii8i 
i.^j7^073 
i.^j8o8/8 

x.9j904ï^ 



916 
917 
919 
919 
9tO 



i'9S9SlH 
19S999^9 
1.5^04708 
X'9609^6t 
x.96l^Hl 



511 
514 



51^ 

517 
518 

530 



554 



i.^^l85»jj 

1.5^15^55 
1.^^184x7 

1.5^5 5 i/J 
i.5^5787« 



t.5f4l/5^ 
15^47505 
1.^^/1017 
1.5^/^710 
1.^^^1417 



1.5^70757 
1.5^7/480 
i.^«8pi/7 
i.^^8481^ 



x.5^85457 
1.5^541/5 
1.^^5881^ 



iV- Logdrith 



554 
55T 
556 
557 
558 



555 

540 
541 
541 
54J 



1-5705465 
1.5708116 

1.57117/8 
1.5717556 
1.5712018 



1.57166/6 
1.5751175 
1-575/856 

1.5740/05 
1-574/1 17 



544 1-5745710 



54/ 
546 

547 
548 



545 
5/0 
5/1 
5/1 
5/5 



1.57/4518 
1.57/8511 
1.576J/00 
1.5768085 



1.5771661 
i->777i3 6 
1.578180J 
1.5786365 
15750515 



5/4 
5// 
5/6 

5/7 
5/8 



5/5 
560 
561 
561 
563 



564 
56/ 
566 
567 



1 575/484 
1.5800034 
1.5804/75 
1.5805115 
1.5813^// 



1.58x8186 
1.5811711 
1.58:17134 

1.58317/1 
1.5836163 



1.5840770 
1-584/173 
1.5845771 
158/416/ 



iV. \L9garith 



567 

568 
565 

570 
571 



571 
573 
574 
975 
576 



577 
57« 
575 



2.58/416/ 
1.58/87/4 
1.5863158 
1.5867717 
1.5871151 



1.5876663 
1.5881128 
1.588//50 
1.5850046 
1.5854458J 



1.5858546 
1-5505385 
1.5507817 



580 '1.551 1161 
58iji.55l6650 



581 1.551111/ 
583I.551//3/ 
584 1.55155/1 
58/ 1.55545^1 
586 1.5558765 



587 
588 
585 
550 



3^-5545171 
15547/65 
1.55/1563 
^•55/63/1 



551 15560757 



551 
553 
554 
99S 
996 



X'996sii7 
^99^9^9X 
1.5575864 
1.5578x51 
1.5581/5/ 



997 ^'99969S^ 
999^-999110$ 
999h-999S6js 

iooot3.ooooooQ 



f*n^ 



looo 



N. 



Logarith 



XOOI 
lQO% 
1005 
1004 

100 S 



lOOé 
ÏOO7 
XOO8 

lOIO 



lOII 

lOIX 

1013 
IOI4 



10X6 

IOI7 
XOI8 

1010 



jx)00434X 
j. 000 8^77 
3.001 500^ 
5.ooJ73)7 

|.001Ié6Z 



3.001/980 
3.003019/ 
3.003460/ 
3.oo389ir 
3.0043114 



IQXX 
lOlt 

X014 

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3.0047/1* 
3.00/180/ 

5.00/6054 
3.0060380 
3 .0064660 



3.0068537 
3.0073105 

3.0077478 
3.oo8i74x 
3.008600X 



3.00501/7 
3.0054/05 
5.005*7;^ 
3.oxx>3ooo! 
3.0107115 



1016 3.011x474 



1017 

IQt8 

1015 
IQ3$ 



IQJX 

X031 
i©34 



3 .01 1/704 
3.OX1553X 
3.0x141/4 
3.0118371 



3.0X3X/87 
3X)X 36757 
3.9x41003 
3.QI4JXO/ 



iV. 



X034 
103/ 
1036 
1037 
1038 



1035 
1040 
1041 
X041 
1043 



Logarith 



3.014/10/ 
3.014^403 

3X>x/3/58 
3.0I/778* 
3.0161574 



3.oi66i//i 
3.0x70333 
3.0174/07 
3.0x78677 
3.0181843 



1044 
104/ 
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XO47 
«048 



104^ 
lO/Q 
XQ/X 
XO/1 
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3.0x8700/ 
3.015x163 

3.0I5./3I7 
5.01554^7 
3.0103613. 



3.01077// 

3.0111853: 
3.01x6017 
3.0110X/7 
3.0114184 



xo/4 3-0x18406 
10// 3.OX3X/X/ 
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10/7 3.0x407/0 
XO/8J3. 0x448/7 



xo/5 
xû6o 
xo6x 

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X064 
106/ 

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3.ox4«y^o! 
3.OX/30/5. 

î-ot/71/4' 

3.0x6x14/ 

06313.0x6/333 



3.01654^ 4^ 

3^7349^1 

3x>i77/7xl 

Xo67t3.oi8x644 l 



N. Logarith 



X067 

xa68 
X065 

X070 
X07X 



Ï071 
1073 
X074 
107/ 
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3.018x644 
3.018/711 

3.0185777 
3^)15383^ 

3^15785/ 



3.030154* 

5*030/557 
3^310043 
1^3140^/ 
5.03x81x3 



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Xo8x 
X083 
1084 
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X087 
1088 



3^34xx7f 
3X>346i8/ 
5.03/0x5^ 
3-05/4*^7 
3.03/8x58 



3.036XX5/ 
3X)f^6x85 



X050 
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3.0574X6/ 

3.0378147 



1051 

10^3 

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105/ 

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3.0381x16 

3.0386X01 

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3.0354I4X 
3.035810^ 



1057 3.040xo(< 

1058 3^4060x1 

X055 3*0405^77 
1x0013^4x35^7 



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1105 
1104 

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2x13 
1114 
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1119 

1X20 



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XX14 
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1117 

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3.0417875] 
5.0411815 
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5'0437J/i 
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3.044/3^8 
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3.04J3230 



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3.04717451 



3.047^^42 
3.0480/31 

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3.0/057^8 
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3.0/1/384 
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3.0/30784 



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1134 

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3.0/4^131 

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3.0/^x413 



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1x40 
1x41 
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3.1567187 
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3-1 041100 

1600 



i6oo 

N. Logarith 



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1604 
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1667 
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1501 
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1367 
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1371 
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3-3741983 
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3.3771140 
3.3773061 
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AU LECTEUR. 

COmme il cft important d'avoir*. des 
Tables trcs-correftes , & qu'il eft diffi- 
cile d'en avoir d'exa£tcs fans y prendre un 
foin particulier j je me fuis efforcé à vous 
lesdonner,MoN cher Lecteur, dans 
la dernière exactitude. Pour cette fin je les 
ay fait imprimer fur celles d'Ulacq , qui ont 
cté imprimées à la Haye en Tannée i66^. & 
qui pafTcnt pour cftre des plus corredes : &c 
je les ay ait fait corriger fur celles du même 
Ulacq , imprimées à Amjfterdam en l'année 
1685. qui partent pour eftre e;ncore plus cor- 
redes que les précédentes, afin de pouvoir 
connoîpre les fautes qui y feroient , lôrfqu'il 
fe rencontreroit quelque différence entre les 
chiffres de l'une & .de J/aùtre de ces deux 
différentes éditions , ce qjni m'a fait décou-^ 
vrir àcs fautes qu'on ne trouvera point icy. 
Et pour une plus grande perfedion , aupa- 
ravant que de faire imprimer ces Tables , 
j'ay préîu avec beaucoup de foin celles 
d'Ulacq , ayant corrigé les Sinus fur les Ta- 
bles de Pitifcus in folio , U les Logarithmes 



auLecteur.' 
fut câix d'Henry Bhggs auifi in folio y ce 
qui m*afaic découYrir quelques; fauces efTeft-- 
tielles , &: plufieurs autres de moindre con« 
fequence , qu^on avoir négligées dans tou- 
tes les redirions , & qu'on ne uouvera point 
dans cellê-cy. Ainû Ton peut s'afTurér d^a* 
voir icy des Tables autant exaâcs qu il eft 
pofliWe*^